R EVIEW LESSONS 4.1 TO 4.4 Honors Geometry. C LASSIFYING T RIANGLES Every triangle can be classified 2 ways: --by the side lengths --by the angle measures.

Slides:

Advertisements

Similar presentations

Chapter 4a: Congruent Triangles By: Nate Hungate, Gary Russell, J. P

Advertisements

Congruent Triangles Geometry Chapter 4.

Identifying Congruent Triangles

Triangles and Congruence

DO NOW 1) X = 180 2) 55 + X = 180 3) X + 58 = 90 4) 31 + X = 90.

Triangles & Their Angles Common Core Investigation 4: Geometry.

4.1 Triangles and Angles.

Applying Triangle Sum Properties

Triangles 1 The Basics. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB∆CBA∆BCA.

Classify Triangles Standard 4C.

Chapter 4 – Congruent Traingles

4.1: Apply Triangle Sum Properties

Chapter 4 Congruent Triangles In this chapter, you will: classify triangles by their parts, apply the Angle Sum Theorem and the Exterior Angle Theorem,

Lesson 4.1 Classifying Triangles Today, you will learn to… * classify triangles by their sides and angles * find measures in triangles.

Chapter 4 Notes. 4.1 – Triangles and Angles A Triangle  Three segments joining three noncollinear points. Each point is a VERTEX of the triangle. Segments.

Triangles & Congruence Advanced Geometry Triangle Congruence Lesson 1.

Classifying Triangles Angle Measures of Triangles.

Triangles 11.2.

Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

Triangle Basics Parts of a Triangle Sides A B C Segment AB, AC, BC Points A, B, C Angles A, B, C Angles Vertices.

Triangle Fundamentals

Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem.

4.1 & 4.2 A Notes. Type of ∆DefinitionPicture Equilateral Triangle CLASSIFICATION BY SIDES All sides are 

Triangle Classification. Objectives Classify triangles by their angle and side measures Find the sum of the measure of the interior and exterior angles.

Goal, to classify triangles by their sides and by their angles.

4-1 Triangles and Angles. Theorem 4.1: Triangle Sum The sum of the measures of the interior angles of a triangle is 180 . xx yy zz  x +

Lesson: Objectives: 4.1 Classifying Triangles  To IDENTIFY parts of triangles  To CLASSIFY Triangles by their Parts.

Triangle Properties - Ch 4 Triangle Sum Conjecture The sum of the measures of the angles of a triangle is…. …180 degrees. C-17 p. 199.

Triangle Congruency Classifying Triangles by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle.

Triangles : a three-sided polygon Polygon: a closed figure in a plane that is made of segments, called sides, that intersect only at their endpoints,

Unit 1B2 Day 2.   Tell whether it is possible to create each of the following:  acute scalene triangle  obtuse equilateral triangle  right isosceles.

GEOMETRY JOURNAL CHAPTER 4 JOSE ANTONIO WEYMANN 9-3 M2 GEOMETRY/ALGEBRA.

Geometry Section 4.1 Triangle Sum Theorem. A triangle is the figure formed by three line segments joining three noncollinear points. A B C.

Chapter 4 Presentation CONGRUENT TRIANGLES. 4.1 Apply Triangle Sum Properties  A triangle is classified by its angles and sides.  Angles: Right=90°

Warm Up # 4 Classify and name each angle. 1 ab c d.

Math 8 Ms. Stewart Unique Triangles.

Triangles and Angles Classifying Triangles. Triangle Classification by Sides Equilateral 3 congruent sides Isosceles 2 congruent sides Scalene No congruent.

Warm Up: Tell whether it is possible to draw each triangle. 1.Acute scalene triangle 2.Obtuse equilateral triangle 3.Right isosceles triangle 4.Scalene.

Classifying Triangles. Two Ways to Classify Triangles  By Their Sides  By Their Angles.

Lesson 8.3 Concept: How to classify triangles by their sides and angles. An equilateral triangle has three sides of the same length. An isosceles triangle.

Triangles and Their Angles Geometry – Section 4.1.

3-4 Angles of a Triangle. A Triangle is a figure formed by three segments joining three noncollinear points. 1) Classifying triangles by their sides.

Classify These Triangles by Sides and Angles. Chapter 4 Congruent Triangles Section 4.1: Triangle Sum Properties Todays Objective: Determine if a right.

Applying Triangle Sum Properties

 Objective: we will be able to classify triangles by their angles and by their sides. A B C The vertices of a triangle are labeled with upper case letters.

Lesson 10-4 Pages Triangles. What you will learn! How to identify and classify triangles.

5-1 Classifying Triangles

Opener: How many diagonals does each polygon have

Geometry 4.1 Triangle and Angles.

Section 3-4 Angles of a Triangle.

CLASSIFICATIONS, ANGLES AND MORE!!

Classifying Triangles

Triangles and Congruence

4.1 Triangles and Angles.

Lesson 3: Parallel Lines and the Triangle Angle-Sum Theorem

Congruent Triangles 4-1: Classifying Triangles

Objectives -triangle names -remote interior -exterior

In conclusion... Same shape, same size Same shape, different size

Classifying Triangles

Unit 4 – Lesson 1 Apply Triangle Sum Properties

Triangles and Angles Section 4.1 and 4.2.

Add up all the sides Perimeter of Area of a Rectangle: ANY polygon:

Lesson 5-1 Angles of Triangles.

Triangle Fundamentals

Classification of Triangles

3-3 Parallel Lines & the Triangle Angle Sum Theorem

4-1 Vocabulary Acute triangle Equiangular triangle Right triangle

4.1 – Apply triangle sum properties

4-1 Classifying Triangles

Lesson 4-R Chapter 4 Review.

Presentation transcript:

R EVIEW LESSONS 4.1 TO 4.4 Honors Geometry

C LASSIFYING T RIANGLES Every triangle can be classified 2 ways: --by the side lengths --by the angle measures

C LASSIFYING T RIANGLES Classification by sides: Equilateral, Isosceles, Scalene Classification by angles: Acute, Equiangular, Right, Obtuse Chart on classification -- textbook page 194

P OSSIBLE NAME COMBINATIONS Acute ScaleneRight Obtuse Acute IsoscelesRight Obtuse EquilateralEquiangular Acute a) Draw each of the seven triangles listed here. b) List the names of at least 2 other triangles that would be impossible to draw. Chart on classification -- textbook page 194 #1

T RIANGLE S UM T HEOREM The three angles of a triangle add up to 180° These expressions represent the angle measures of a triangle. Find the measure of each angle, then classify the triangle by its angles. m  K = 10(x + 1)° m  L = (9x – 3)° m  M = (7x – 9)° #2

E XTERIOR A NGLE T HEOREM The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. # m  1 + m  2 = m  3 Find the measure of the exterior angle shown below. 110° (4x – 7)° x°

C ONGRUENT T RIANGLES Congruent triangles are the same size and shape Angles that are the same size are called corresponding angles. Sides that are the same length are called corresponding sides. When writing a congruence statement, the order of the letters matters. For example, the statement ∆XYZ  ∆STR, tells us all of the following:  X  S,  Y  T,  Z  R and Segments XY and ST are congruent, as are segments YZ and TR and segments XZ and SR

U SING PROPERTIES OF CONGRUENT FIGURES In the diagram ABCD  KJHL. Find the value of x and y. #4 AB C D K J H L 91° 86° 113° 9 cm 6 cm (4x – 3) (5y – 12)°

U SING PROPERTIES OF CONGRUENT FIGURES Find the value of x. Write a congruence statement for the two triangles. #5 A B C D E F 22° 87° (4x + 15)°

C ONGRUENCE S HORTCUTS We have learned 4 shortcuts for proving triangles are congruent: SSS, SAS, ASA, AAS. For each of the following, tell if there is enough information to prove the triangles are congruent. If so, tell which congruence shortcut you would use. AB #6

A NSWERS 2. x = 7, m  K = 80°, m  L = 60°, m  M = 40°, acute 3. x = 39, 149° 4. x = 3, y = x = 14, ∆ABC  ∆DEF 6. A yes, SAS B yes, AAS