C. N. Colón Geometry St. Barnabas HS Bronx, NY Rays and Angles Ch. 1.5 and 1.6.

Slides:

Advertisements

Similar presentations

Lines, Segments, and Rays. Line  A line is perfectly straight and extends forever in both directions. Any two points on the line can be used to name.

Advertisements

Adjacent, Vertical, Supplementary, Complementary and Alternate, Angles.

a location in space that has no size.

ANGLES Geometry 1.3a. State Standard: LG.1.G.4Geometry Apply, with and without appropriate technology, definitions, theorems, properties, and postulates.

1Geometry Lesson: Rays, Angles Aim: Do Now: Ans. M(4, -8) Ans. 10 What are rays and angles?

Warm Up:. Linear Pair I: Two angles that share a common vertex and together make a straight line (180°). M: What is the missing measure?

Basic Definitions in Geometry

 RAY  RAY: Defined as …Ray AB is part of line AB that contains Point A and all the points on line AB that are on the same side of point A as point B.

Angle Relationships.

Angle Pair Relationships

C. N. Colón Geometry St. Barnabas HS Bronx, NY Rays and Angles Ch. 1.5 and 1.6.

Angles (def) An ACUTE ANGLE is an angle w/ a MEASURE less than 90° (def) A Right angle is an angle w/ a MEASURE = 90° (def) An Obtuse angle is an angle.

Geometry Vocabulary Lesson #3. #12 Angle A figure formed by 2 rays with the same endpoint.

Objectives-What we’ll learn…

Measure and classify Angles

Bell Work In your group, solve the following problems. The color indicate the person that’ll write the answer to the question. (4 questions about line.

Geometry Ch 1.1 Notes Conjecture – is an unproven statement that is based on observation Inductive Reasoning – is a process used to make conjectures by.

GEOMETRY PRE-UNIT 4 VOCABULARY REVIEW ALL ABOUT ANGLES.

Geometrical Jeopardy Basic GeoAnglesTrianglesQuadsPolygons

Mrs. McConaughyGeometry1 Introduction to Proof: During this lesson, we will:  Identify angles as adjacent or vertical  Identify supplementary and complementary.

Section 2.7 PROVE ANGLE PAIR RELATIONSHIPS. In this section… We will continue to look at 2 column proofs The proofs will refer to relationships with angles.

Angle Relationships Section 1-5 Adjacent angles Angles in the same plane that have a common vertex and a common side, but no common interior points.

SPECIAL PAIRS OF ANGLES. Congruent Angles: Two angles that have equal measures.

Angles Acute angle (def)- angle measure less than 90° Right angle (def)- angle measure= 90° Obtuse angle (def)- angle measure greater than 90° Straight.

Angle Relationships Geometry 1.5.

Math I CAN find the measure of angles. I CAN construct angles.

Hosted by Mrs. Smyth 1pt 2pt 4pt 3pt 4pt LinesAnglesMore LinesAngles Too 3pt 2pt 4pt 2pt 1pt 5pt 1pt.

Geometry 1-3 Measuring and Constructing Angles. Vocabulary Angle- a figure formed by two rays, or sides, with a common endpoint. Vertex- The common endpoint.

9.1 Angles By: Francisco May 26, 2006 Ms. Montilla.

Measuring Angles. Geometry vs Algebra Segments are Congruent –Symbol [  ] –AB  CD –  1   2 Lengths of segments are equal. –Symbol [ = ] –AB = CD.

Ch 1.4.  Different kinds of angles.  Angle relationships and how they can be used to apply algebraic concepts.

Measuring Angles Geometry Mrs. King Unit 1, Lesson 5.

Chapter 1 - Section 3 Special Angles. Supplementary Angles Two or more angles whose sum of their measures is 180 degrees. These angles are also known.

Angle Measure Section 1-4. angle – a figure consisting of 2 noncollinear rays with a common endpoint. The 2 rays are called the sides of the angle. The.

Angle and Triangle Flash Cards

Angle and Triangle Flash Cards

Geometry Vocabulary Point an exact location in space Line A straight path that goes on forever in both directions A and B are any 2 points on the line.

Types of Angles A right angle has a measure of 90 degrees. An acute angle has a measure of less than 90 degrees. An obtuse angle has a measure greater.

Geometry Section 1.4 Angles and Their Measures. An *angle is the figure formed by the union of two rays with a common endpoint. The rays are called the.

Example 1.Name all angles with B as a vertex. 2. Name the sides of angle Write another name for angle 6.

Angles  Learn to name and measure angles.. Lines and Rays: A Ray is part of a line. A Ray has one initial point and extends indefinitely in one direction.

CHAPTER 1: Tools of Geometry Section 1-6: Measuring Angles.

Geometry Notes. The Language of Geometry Point: A point is a specific location in space but the point has no size or shape Line: a collection of points.

Unit 1 All About Angles and Constructions (not necessarily in that order) Ms. Houghton Geometry Honors Fall 2014.

Chapter By Skyler Cassity & Ryan Tourial.

Lines and Angles Ray Congruent Equal in size and shape.

Welcome to Geometry Unit 1 Vocabulary. Undefined Terms Point In Euclidean geometry, a point is undefined. You can think of a point as a location. A point.

Chapter 5.2 & 5.3 BISECTORS, MEDIANS AND ALTITUDES.

Angles Project Endiya, Nick, and Mason 5th period Let’s get learning…

GEOMETRY UNIT 3 VOCABULARY ALL ABOUT ANGLES. ANGLE DEFINITION Angle A figure formed by two rays with a common endpoint.

DO NOW Constructing a Segment Bisector Draw ST on your transparency paper. Fold the paper so point S is lying on point T. In the crease draw a dotted line.

ANGLE RELATIONSHIPS Mrs. Insalaca 8 th Grade Math.

Bell Ringer: Quiz Review 1.) Define a.) Collineard.) Obtuse b.) Coplanare.) Right c.) Acute Solve for x 2.) 3.) A B C 2x AC = 8X + 4 A B C D 3x +

Angles #29 Acute angle (def)- angle less than 90° # 28 Right angle (def)- angle = 90° #30 Obtuse angle (def)- angle greater than 90° #31 Straight angle.

What kind of angle is

Measures and Relationships.  Ray – part of a line that includes one endpoint and extends infinitely in one direction  Opposite rays – rays that share.

Geometry Basic Terms Unit 1 Vocabulary.

Objective: To recognize and classify angles and

Topic 1-5 Angle Relationships.

Geometry vocab. tHESE SHOULD also be DONE ON INDEX CARDS AND YOU SHOULD BE CONSTANTLY REVIEWING THEM AS WE GO!

*YOU SHOULD CONSTANTLY BE REVIEWING THIS VOCABULARY AS WE GO!

G-CO.1.1, G-CO.1.2, G-Co.1.4, G-CO.1.5, G-CO.4.12, G-CO.3.9

Measures and Relationships

Chapter 2 : Angles Vocabulary Terms.

Exploring Angles and Angle Relationships

PLANE A plane is a FLAT surface made up of points that extends indefinitely in all directions. Symbolic Notation: Plane V.

Aim: Do Now: What are rays and angles? Ans. M(4, -8) Ans. 10

Coordinate Distance Congruent Midpoint Bisector Angle Sides Vertex

Presentation transcript:

C. N. Colón Geometry St. Barnabas HS Bronx, NY Rays and Angles Ch. 1.5 and 1.6

A RAY consists of a point on a line and all points on one side of the point. K A D ● ● This ray can be called AK or AD The beginning of the name is the endpoint, A.

Opposite rays are two rays of the same line with a common endpoint and no other points in common RAY C●C● T●T● A

Oh, Mrs. C, you are tooooooo funny!

This is an angle

A n angle is a set of points that is the union of two rays having the same endpoint A n Side Vertex D●D● E●E● There are several ways to name this angle: A DAE EAD n

In this case there is no confusion you name an angle by the vertex. A A

obtuse angle: greater than 90° acute angle: less than 90°

A B C D How many angles do you see? A – 1 B – 2 C – 3 D – Huh?

Degrees were developed by the Babylonians thousands of years ago. They divided a circle into 360 parts and called each part one degree.

The symbol for degrees, as you probably already know, is a small superscript circle. 45°37°112°

This is an acute angle and it measures 62º

This is an obtuse angle and it measures 128º

A: 180B: 125C: 50D: 25

Angles are congruent if they have the same measure. A B

If point S is in the interior (middle) of angle PQR, then the measure of PQS + measure of SQR = measure of PQR P Q R S

P Q R S The bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent angles. PQS = SQR ~

Complementary angles are two angles that total 90 degrees 30º and ___ 27º and ___ 12º and ___ 63º 60º 78º

Supplementary angles are two angles that total 180 degrees 25º and ___ 67º and ___ 124º and ___ 155º 56º 113º

AngleComplementSupplement 28º 49º 67º 100º 147º

AngleComplementSupplement 28º62º 49º 67º 100º 147

AngleComplementSupplement 28º62º152º 49º 67º 100º 147º

AngleComplementSupplement 28º62º152º 49º41º 67º 100º 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º 100º 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º 100º 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100º 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147º

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147ºnone

AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147ºnone33º

Linear angles are two angles that share a side and make a line. Linear angles total 180°

Right angles are angles that measure 90°

Acute angles angles that measure less than 90°

Obtuse angles are angles that measure more than 90° but less than 180°

Straight angle is an angle that makes a straight line and measures 180º

Perpendicular lines are lines that intersect to form right angles. The distance from any point to a line is the length of the perpendicular from the point to the line.

A reflex angle is an angle that measures more than 180°

Read p , p. 18 # 3-5 (all) Read p , p. 21 #3-20 (e)