Unit 2: Congruence, Similarity, and Proofs

Unit 2: Congruence, Similarity, and Proofs
Vocabulary Builder

Daily Agenda Parallel Transversal Intersect Perpendicular
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Parallel Transversal Intersect Perpendicular

Daily Agenda Perpendicular Parallel Parallel Intersect
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Perpendicular Parallel Parallel Intersect

Perpendicular bisector
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 9. 10. 11. 12. 13. 14. 15. 16. 17. Perpendicular lines Is perpendicular to Congruent segments Perpendicular bisector Midpoint Parallel lines Is greater than arc Angle bisector

Daily Agenda compass arc intersects compass arc January 25, 2017
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda compass arc intersects compass arc

Daily Agenda compass arc arc straightedge January 25, 2017
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda compass arc arc straightedge

Daily Agenda Supplementary angles Complementary angles Vertical angles
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Supplementary angles Complementary angles Vertical angles Adjacent angles Angle bisector

January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda similar Similarity transformation composition dilation Scale factor

January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda reflection Line of reflection translation

2.1 Precise Definitions

Daily Agenda Precise Definitions Line segment angle January 25, 2017
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? Precise Definitions Daily Agenda Line segment angle

2.1 Precise Definitions Daily Agenda January 25, 2017 ACUTE ACUTE
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda ACUTE ACUTE ACUTE OBTUSE RIGHT RIGHT OBTUSE ACUTE ACUTE RIGHT ACUTE OBTUSE ACUTE RIGHT OBTUSE OBTUSE

2.1 Precise Definitions Daily Agenda circle center radius
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda circle center radius Parallel lines Perpendicular lines Midpoint Two congruent parts

2.1 Precise Definitions Daily Agenda January 25, 2017 TRUE FALSE FALSE
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

2.1 Precise Definitions Daily Agenda Divides into equal parts
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda Divides into equal parts Angle bisector Congruent angles Adjacent angles Vertical angles equal congruent Complementary angles 90 complement Supplementary angles 180 supplement

2.1 Precise Definitions Daily Agenda January 25, 2017 VERTICAL
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda VERTICAL ADJACENT 152 114 58

2.1 Precise Definitions Daily Agenda January 25, 2017 COMPLEMENTARY
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda COMPLEMENTARY ADJACENT ADJACENT SUPPLEMENTARY LINEAR PAIR 25 26 25

2.1 Precise Definitions Daily Agenda January 25, 2017
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda

2.1 Precise Definitions Daily Agenda 180 Interior angle Exterior angle
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda 180 Interior angle Exterior angle Remote interior angle

2.1 Precise Definitions Daily Agenda January 25, 2017 63 75 20 55 23
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda 63 75 20 55 23 17

2.1 Precise Definitions Daily Agenda Isosceles Triangle legs
January 25, 2017 Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Isosceles Triangle Daily Agenda legs Vertex angle Base angles Isosceles Triangle Theorem

2.1 Precise Definitions Daily Agenda January 25, 2017 12 35 15 12 36 9
Today’s Date G.CO.1 Experiment with transformations in the plane Use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined terms What am I learning today? Vocabulary Builder What am I going to do today? Daily Ticket out the Door How will I show you that I’ve learned it? 2.1 Precise Definitions Daily Agenda 12 35 15 12 36 9

2.1 Precise Definitions (Continued…)

Checking for Understanding
Lesson 1: Precise Definitions

4 In the diagram of ABC, 𝐴𝐵 is extended to D, exterior angle CBD measures 145˚ and mC = 75. What is the measure of CAB? 35 70 Solution: B 110 220 Copyright© 2015 EducAide Software Inc. All rights reserved.

2.2 Constructions of Lines and Angles

2.2 Constructions of Lines and Angles
January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda construction compass straightedge

Daily Agenda 2.2 Constructions of Lines and Angles
Segment bisector January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it?

Daily Agenda Congruent segments January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Tick marks Congruent angles Arc marks

Daily Agenda January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it?

Daily Agenda perpendicular bisector January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? perpendicular Distance from a point on a line

Daily Agenda January 26, 2017 Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Construction: Congruent Segment Construction: Segment Bisector (using patty paper) Construction: Congruent Angle Construction: Angle Bisector Construction: Parallel Lines Construction: Perpendicular Bisector

Daily Agenda January 26, 2017 G.CO.12 Make geometric constructions
Today’s Date G.CO.12 Make geometric constructions Make formal geometric constructions with a variety of tools and methods What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it?

Lesson 2: Constructions of Lines and Angles

2.3 Constructions of Polygons

2.3 Construction of Polygons
January 27, 2017 Today’s Date G.CO.13 Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle What am I learning today? Construct a Square, Hexagon, and an Equilateral Triangle Inscribed in a Circle What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Regular polygon equiangular equilateral angles sides equilateral triangle Congruent

January 27, 2017 Today’s Date G.CO.13 Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle What am I learning today? Construct a Square, Hexagon, and an Equilateral Triangle Inscribed in a Circle What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Squares 90˚

January 27, 2017 Today’s Date G.CO.13 Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle What am I learning today? Construct a Square, Hexagon, and an Equilateral Triangle Inscribed in a Circle What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda hexagon inscribed vertex

January 27, 2017 Today’s Date G.CO.13 Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle What am I learning today? Construct a Square, Hexagon, and an Equilateral Triangle Inscribed in a Circle What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Construction 1: Regular Hexagon Construction 2: Equilateral Triangle (same as hexagon) Construction 3: Square Construction 4: Incircle

January 27, 2017 Today’s Date G.CO.13 Make geometric constructions Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle What am I learning today? Construct a Square, Hexagon, and an Equilateral Triangle Inscribed in a Circle What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Lesson 3: Constructions of Polygons

2 Which of the following constructions represent the picture below. Constructing a Square Inscribed in a Circle Constructing a Triangle Inscribed in a Circle Constructing a Circle Inscribed in a Triangle Constructing a Hexagon Inscribed in a Circle B Copyright© 2015 EducAide Software Inc. All rights reserved.

3 Consider the beginning of a construction of a square inscribed in circle Q. Step 1: Label point R on circle Q Step 2: Draw a diameter through R and Q Step 3: Label the intersection on the Circle point T What is the next step in this construction? Draw radius 𝑆𝑄. B or D Label point S on circle Q. Construct a line segment parallel to 𝑅𝑇 Construct the perpendicular bisector of 𝑅𝑇 Copyright© 2015 EducAide Software Inc. All rights reserved.

Use the diagram to answer the question. Daja is drawing a square inscribed in a circle using a compass and a straightedge two steps are shown. Which is the best step for Daja to do next? 4 D Copyright© 2015 EducAide Software Inc. All rights reserved.

5 In the design, a hexagon is inscribed in a circle. Which point shows the location of Point Q after a 240˚ clockwise rotation around the center? S T U C V Copyright© 2015 EducAide Software Inc. All rights reserved.

2.4 Corresponding Parts

Daily Agenda 2.4 Corresponding Parts January 29, 2017
Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Corresponding angles Corresponding sides congruent

Daily Agenda 2.4 Corresponding Parts T 𝑩𝑪 A 𝑨𝑩 𝑹𝑻 S Q 𝑹𝑺 QRS 𝑺𝑸
January 29, 2017 Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda T 𝑩𝑪 A 𝑨𝑩 𝑹𝑻 S Q 𝑹𝑺 QRS 𝑺𝑸 𝑸𝑹 QSR

Daily Agenda 2.4 Corresponding Parts January 29, 2017 𝑨𝑪 ≅ 𝑩𝑫 𝑱𝑴 ≅ 𝑲𝑳
Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 𝑨𝑩 ≅ 𝑱𝑲 𝑨𝑪 ≅ 𝑩𝑫 𝑱𝑴 ≅ 𝑲𝑳 𝑩𝑪 ≅ 𝑲𝑳 𝑨𝑩 ≅ 𝑪𝑫 𝑲𝑱 ≅ 𝑳𝑴 𝑨𝑪 ≅ 𝑱𝑳 𝑩𝑪 ≅ 𝑩𝑪 𝑲𝑴 ≅ 𝑲𝑴 ∠𝑨≅∠𝑫 ∠𝑱≅∠𝑳 ∠𝑨≅∠𝑱 ∠𝑩≅∠𝑲 ∠𝑨𝑩𝑪≅∠𝑫𝑪𝑩 ∠𝑨𝑩𝑪≅∠𝑫𝑪𝑩 ∠𝑪≅∠𝑳 ∠𝑨𝑪𝑩≅∠𝑫𝑩𝑪 ∠𝑨𝑪𝑩≅∠𝑫𝑩𝑪

Daily Agenda 2.4 Corresponding Parts January 29, 2017 𝑹𝑺 ≅ 𝑺𝑻 𝑬𝑮 ≅ 𝑳𝑱
Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 𝑹𝑺 ≅ 𝑺𝑻 𝑬𝑮 ≅ 𝑳𝑱 𝑨𝑪 ≅ 𝑩𝑫 𝑹𝑼 ≅ 𝑻𝑼 𝑭𝑮 ≅ 𝑳𝑲 𝑨𝑩 ≅ 𝑪𝑫 𝑺𝑼 ≅ 𝑺𝑼 𝑭𝑬 ≅ 𝑲𝑱 𝑩𝑪 ≅ 𝑩𝑪 ∠𝑹≅∠𝑫 ∠𝑭≅∠𝑲 ∠𝑨≅∠𝑫 ∠𝑹𝑼𝑺≅∠𝑻𝑼𝑺 ∠𝑬≅∠𝑱 ∠𝑨𝑩𝑪≅∠𝑫𝑪𝑩 ∠𝑺𝑼𝑹≅∠𝑺𝑼𝑻 ∠𝑮≅∠𝑳 ∠𝑨𝑪𝑩≅∠𝑫𝑩𝑪

Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Daily Agenda 2.4 Corresponding Parts Rigid Motion Isometry lengths
January 29, 2017 Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Rigid Motion Isometry lengths Angle measure image Pre-image congruent transformation

Daily Agenda 2.4 Corresponding Parts yes Translation
January 29, 2017 Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda yes Translation T(x, y) = (x – 5, y + 1) no Dilation D(x, y) = (1.5x, 1.5y)

Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Lesson 4: Corresponding Parts

2.5 Congruent Triangles

Daily Agenda 2.5 Congruent Triangles congruent angles sides congruence
January 31, 2017 Today’s Date G.CO.9 Prove geometric theorems Prove theorems about lines and angles (Vertical angles, Relationships with Transversals What am I learning today? Copy a Segment, Construct a Segment Bisector Copy an Angle, Construct an Angle Bisector Construct Parallel Lines and Perpendicular Bisector What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda congruent angles sides congruence

Daily Agenda 2.5 Congruent Triangles January 31, 2017 SAS no SSS SAS
Today’s Date G.CO8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence follow from the definition of congruence from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda SAS no ∆𝑷𝑹𝑺≅∆𝑷𝑸𝑺 SSS SAS ∆𝑷𝑸𝑹≅∆𝑺𝑻𝑼 ∆𝑨𝑩𝑬≅∆𝑪𝑩𝑫 SAS ∆𝑴𝑳𝑵≅∆𝑶𝑵𝑳 SSS ∆𝑾𝑿𝑽≅∆𝒀𝑿𝒁

Daily Agenda 2.5 Congruent Triangles January 31, 2017 SAS SSS SAS SAS
Today’s Date G.CO8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence follow from the definition of congruence from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda SAS SSS ∆𝑨𝑩𝑫≅∆𝑪𝑩𝑫 ∆𝑨𝑬𝑹≅∆𝑾𝑫𝑮 SAS SAS ∆𝑯𝑰𝑱≅∆𝑯𝑮𝑬 ∆𝑷𝑹𝑺≅∆𝑷𝑸𝑺 SSS SAS ∆𝑷𝑹𝑺≅∆𝑷𝑸𝑺 ∆𝑷𝑹𝑺≅∆𝑷𝑸𝑺

Daily Agenda 2.5 Congruent Triangles January 31, 2017
Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it?

Daily Agenda 2.5 Congruent Triangles January 31, 2017 ASA AAS
Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? ASA AAS NOT CONGRUENT ∆𝑺𝑽𝑿≅∆𝑻𝑽𝑹 ∆𝑩𝑻𝑹≅∆𝑨𝑪𝑹

Daily Agenda 2.5 Congruent Triangles January 31, 2017 NOT CONGRUENT
Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? NOT CONGRUENT AAS ∆𝑫𝑬𝑭≅∆𝑰𝑮𝑯 ASA ∆𝑺𝑹𝑻≅∆𝑾𝑽𝑿 AAA ∆𝑫𝑬𝑭≅∆𝑮𝑰𝑯

Daily Agenda 2.5 Congruent Triangles ∠𝑹≅∠𝑫 ∠𝑩≅∠𝑺 𝑶𝑴 ≅ 𝑩𝑨 𝒐𝒓 𝑶𝑵 ≅ 𝑪𝑨
January 31, 2017 Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? ∠𝑹≅∠𝑫 ∠𝑩≅∠𝑺 𝑶𝑴 ≅ 𝑩𝑨 𝒐𝒓 𝑶𝑵 ≅ 𝑪𝑨 𝑿𝒁 ≅ 𝑪𝑩

Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it?

Today’s Date G.CO.8 Understand congruence in terms of rigid motions Explain how the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) follow from the definition of congruence in terms of rigid motions What am I learning today? Congruent Triangles What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Lesson 5: Congruent Triangles

2.6 Similar Figures

Daily Agenda 2.6 Similar Figures ratio = 0 proportion equal 𝒂𝒅=𝒄𝒅 𝟑 𝟒
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda ratio = 0 proportion equal 𝒂𝒅=𝒄𝒅 𝟑 𝟒 𝟏 𝟕 𝟐 𝟑 16 4 24

Daily Agenda 2.6 Similar Figures 𝟒 𝟓 𝟒 𝟓 𝟏 𝟐 36 10 33 February 1, 2017
Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 𝟒 𝟓 𝟏 𝟐 𝟒 𝟓 36 10 33

Daily Agenda 2.6 Similar Figures similar shape size congruent
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda similar shape size congruent proportional 𝟑 𝟔 = 𝟒 𝟖 𝟐 𝟓 𝒚𝒆𝒔 𝒚𝒆𝒔

Daily Agenda 2.6 Similar Figures 𝟐𝟎 𝟑𝟎 = 𝟐𝟎 𝒙 𝟔 𝟏𝟐 = 𝒙 𝟏𝟔 x = 30 x = 8
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 𝟐𝟎 𝟑𝟎 = 𝟐𝟎 𝒙 𝟔 𝟏𝟐 = 𝒙 𝟏𝟔 x = 30 x = 8 𝟐𝟎 𝟑𝟎 = 𝟐𝟎 𝒚 𝟔 𝟏𝟐 = 𝒚 𝟐𝟎 y = 30 y = 10

Daily Agenda ~ 2.6 Similar Figures Similarity statement
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda Similarity statement ~ Similarity ratio lengths 𝟖 𝟔 = 𝟒 𝟑 15 9

Daily Agenda 2.6 Similar Figures 𝒙 𝟗 = 𝟖 𝟏𝟐 x = 6 𝟏𝟎 𝟓 = 𝟒.𝟓 𝒙
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.6 Similar Figures 𝒙 𝟗 = 𝟖 𝟏𝟐 x = 6 𝟏𝟎 𝟓 = 𝟒.𝟓 𝒙 x = 2.25 𝟏𝟐 𝟏𝟖 = 𝒙+𝟏 𝟐𝟒 x = 15 𝟒𝟎 𝟑𝟎 = 𝒙+𝟏𝟓 𝟏𝟖 x = 9

Daily Agenda 2.6 Similar Figures February 1, 2017
Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Daily Agenda 2.6 Similar Figures BC = 10 Perimeter = 16 + 12 +10
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda BC = 10 Perimeter = Perimeter = 38

Daily Agenda 2.6 Similar Figures 2x - 6 = 𝟏 𝟐 (𝟏𝟖) x = 7.5 ED = 11.5
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2x - 6 = 𝟏 𝟐 (𝟏𝟖) x = 7.5 ED = 11.5 x = 6

Daily Agenda 2.6 Similar Figures 𝑨𝑬 𝑬𝑩 = 𝑨𝑭 𝑭𝑪 𝑬𝑭 ∥ 𝑩𝑪
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.6 Similar Figures 𝑨𝑬 𝑬𝑩 = 𝑨𝑭 𝑭𝑪 𝑬𝑭 ∥ 𝑩𝑪

Daily Agenda 2.6 Similar Figures 𝑨𝑪 𝑪𝑬 = 𝑩𝑫 𝑫𝑭 February 1, 2017
Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.6 Similar Figures 𝑨𝑪 𝑪𝑬 = 𝑩𝑫 𝑫𝑭

Lesson 6: Similar Polygons

2.7 Similar Figures

2.7 Dilations and Similarity
February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.7 Dilations and Similarity dilation Center of dilation inside on outside similar Angle measure length proportional multiply Scale factor enlargement reduction

February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.7 Dilations and Similarity A B A’ B’ Scale Factor = −𝟐 −𝟒 𝑺.𝑭. = 𝟏 𝟐 Center of Dilation (0,0)

February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda 2.7 Dilations and Similarity Scale Factor = −𝟕.𝟓 −𝟓 𝑺.𝑭. = 𝟑 𝟐 =𝟏.𝟓 A B C Center of Dilation (0,0) A’ B’ C’

February 1, 2017 Today’s Date G.SRT.1 Understand similarity in terms of similarity Transformations Verify experimentally the properties of dilations given by a center and a scale factor What am I learning today? Similar Figures Similar Polygons What am I going to do today? 5 Question Daily Assessment Daily Ticket out the Door How will I show you that I’ve learned it? Daily Agenda

Lesson 7: Dilations and Similarity

4 C

5 A

Unit 2: Congruence, Similarity, and Proofs

Similar presentations

Presentation on theme: "Unit 2: Congruence, Similarity, and Proofs"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Unit 2: Congruence, Similarity, and Proofs

Similar presentations

Presentation on theme: "Unit 2: Congruence, Similarity, and Proofs"— Presentation transcript:

Similar presentations

About project

Feedback