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

Slides:

Advertisements

Similar presentations

2-5 Proving Angles Congruent

Advertisements

Defined Terms and Postulates April 3, Defined terms Yesterday, we talked about undefined terms. Today, we will focus on defined terms (which are.

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.

Proving Angles Congruent.  Vertical Angles: Two angles whose sides form two pairs of opposite rays; form two pairs of congruent angles

Proving Angles Congruent

Geometric Terms 7 Math: Sections 7-1 and 7-2. Lines and Planes Point - indicates a location in space. Line - A series of points that extend forever in.

1.5 Exploring Angle Pairs 9/20/10

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.

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

Angle Relationships.

Angle Pair Relationships

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.

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 PRE-UNIT 4 VOCABULARY REVIEW ALL ABOUT ANGLES.

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.

Geometry Section 1.5 Describe Angle Pair Relationships.

Geometry Section 1.6 Special Angle Pairs. Two angles are adjacent angles if Two angles are vertical angles if.

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.

Section 1-5: Exploring Angle Pairs Objectives: Identify special angle pairs & use their relationships to find angle measures.

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

Ray An object that has one endpoint and continues infinitely in ONE direction.

Chapter 13 L13-1 Notes: Angles. Vocabulary Angles have two sides that share a common endpoint called the vertex of the angle.

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

Proving Angles Congruent

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

PROVING ANGLES CONGRUENT. Vertical angles Two angles whose sides form two pairs of opposite rays The opposite angles in vertical angles are congruent.

Line and Angle Relationships Sec 6.1 GOALS: To learn vocabulary To identify angles and relationships of angles formed by tow parallel lines cut by a transversal.

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.

Geometry Angle Vocabulary Review – Chapter 1. Name and ID parts of angles A B C D E F 1.Name an angle in different ways. 2.ID the vertex of an angle.

Chapter 1 Exploring Geometry: Points, Lines, and Angles in the Plane

Honors Geometry Section 1.3 part2 Special Angle Pairs.

Section 1-4 Angles and their Measures. Angle Formed by two rays with a common endpoint –T–The rays are the sides of the angle –T–The common endpoint is.

Geometry Vocabulary Introduction to Classifying Angles.

Defining Terms This statement defines a protractor: “A protractor is a geometry tool used to measure angles.” First, you classify what it is (a geometry.

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.

OBJECTIVES: 1) TO IDENTIFY ANGLE PAIRS 2) TO PROVE AND APPLY THEOREMS ABOUT ANGLES 2-5 Proving Angles Congruent M11.B C.

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.

Section 2.5: Proving Angles Congruent Objectives: Identify angle pairs Prove and apply theorems about angles.

How do you measure, name and classify angles? What is the Angle Addition Postulate? How do you identify angle pairs? Chapter 1 Section 1.6.

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.

ANGLE RELATIONSHIPS Mrs. Insalaca 8 th Grade Math.

Measuring Angles 1-6. Angles  An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is called the.

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 +

Proving the Vertical Angles Theorem (5.5.1) May 11th, 2016.

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.

Angle Pair Relationships and Angle Bisectors. If B is between A and C, then + = AC. Segment Addition Postulate AB BC.

GEOMETRY HELP Name the angle below in four ways. The name can be the vertex of the angle: G. Finally, the name can be a point on one side, the vertex,

2.6 Proven Angles Congruent. Objective: To prove and apply theorems about angles. 2.6 Proven Angles Congruent.

Geometry Basic Terms Unit 1 Vocabulary.

1-4: Measuring Angles.

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

1-5 Angle Relations.

Chapter 2 : Angles Vocabulary Terms.

Exploring Angles and Angle Relationships

Exploring Angle Pairs Skill 05.

Identifying Angle Pair Relationships

Sections 1.4 and 1.5 Brit Caswell.

Geometry Exploring Angle Pairs.

Presentation transcript:

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

Objectives  To find the measures of angles.  To identify special pairs of angles.

Vocabulary  Angle  Acute Angle  Right Angle  Obtuse Angle  Straight Angle  Congruent Angles  Vertical Angles  Adjacent Angles  Complementary Angles  Supplementary Angles

Angle  An angle is formed by two rays with the same endpoint.  The rays are the “sides” of the angle.  The common endpoint is the “vertex.”

Ways to name an angle:  Using only the vertex.  However, we can only do this if there is only one angle with that vertex.  Using three points.  When we do this, the vertex must be listed in the middle.  Using the assigned number.

Postulate 1-7: “The Protractor Postulate”

Classifying Angles  Acute Angle- an angle less than 90 degrees.  Right Angle- an angle that is exactly 90 degrees.  Obtuse Angle- an angle with a measure greater than 90 degrees but less that 180 degrees.  Straight Angle- an angle that is exactly 180 degrees.

Congruent Angles  Angles with the same measure are congruent angles.

Postulate 1-8: “The Angle Addition Postulate”  If point B is in the interior of R AOC then:  m R AOB + m R BOC = m R AOC

Vertical Angles  Vertical angles are two angles whose sides are opposite rays.

Adjacent Angles  Adjacent angles are two coplanar angles with a common side, common vertex, but no common interior points.

Complementary Angles  Complementary angles are two angles whose measures have a sum of 90 degrees.  Each angle is called the “compliment” of the other.

Supplementary Angles  Supplementary angles are two angles whose measures have a sum of 180 degrees.  Each angle is called the “supplement” of the other.

Identifying Angle Pairs  Identify the pairs of numbered angles that are related as follows:  Complementary  Supplementary  Vertical  Adjacent

Making Conclusions from Diagrams  We can always conclude the following:  Adjacent angles  Adjacent supplementary angles  Vertical angles  We cannot assume unless we are told:  Angles (or segments) are congruent  An angle is a right angle  Lines are parallel  Lines are perpendicular

Making Conclusions: True or False?  R 1 and R 4 are vertical?  R 1 and R 5 are supplementary?  R 3 is a right angle?  R 2 and R 3 are adjacent?  R 1 and R 2 are congruent?