PROVING ANGLES CONGRUENT. Vertical angles Two angles whose sides form two pairs of opposite rays 1 2 3 4 The opposite angles in vertical angles are congruent.

Slides:

Advertisements

Similar presentations

2-5 Proving Angles Congruent

Advertisements

Adjacent, Vertical, Supplementary, and Complementary Angles

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

Standard 2.0, 4.0.  Angles formed by opposite rays.

Proving Angles Congruent

Lesson 9.2 Angle Relationships and Parallel Lines

1.5 Exploring Angle Pairs 9/20/10

1-5: Exploring Angle Pairs. Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles Two coplanar angles with a:

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?

Bellringer Your mission: Construct a perfect square using the construction techniques you have learned from Unit 1. You may NOT measure any lengths with.

Angle Pair Relationships

Section 1.6 Pairs of Angles

2.3 Complementary and Supplementary Angles

Objectives-What we’ll learn…

1-5 Angle Relationships What are: adjacent angles linear pairs

1.5 Describe Angle Pair Relationships

Angle Pair Relationships

1-5 Angle Relationships What are: adjacent angles linear pairs

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.

L.T. I can identify special angle pairs and use their relationships to find angle measure.

UNIT 01 – LESSON 06 – ANGLE RELATIONSHIPS Essential Question How can you describe angle pair relationships and use thee descriptions to find angle measures?

Daily Warm-Up Quiz 1.Name the same ray two different ways. T E A M 2.Draw the next picture/number in the picture pattern: “measure of line segment UP =

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

Proving Angles Congruent

Proving angles congruent. To prove a theorem, a “Given” list shows you what you know from the hypothesis of the theorem. You will prove the conclusion.

1.4 Pairs of Angles Adjacent angles- two angles with a common vertex and common side. (Side by side) Linear pair- a pair of adjacent angles that make a.

1.5 Exploring Angle Pairs.

2-4 Special Pairs of Angles Objectives -Supplementary Angles Complementary Angles -Vertical angles.

Section 1-6 Angle Pair Relationships. Vertical angles Formed when two lines intersect. Vertical Angles are Congruent. 1 2.

- is a flat surface that extends in all directions. Objective - To identify angles as vertical, adjacent, complementary and supplementary. Plane.

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

Special angles, perpendicular lines, and parallel lines and planes September 10, 2008.

2-5 Proving Angles Congruent Angle Pairs Vertical Angles two angles whose sides form two pairs of opposite rays Adjacent Angles two coplanar angles.

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

2.4: Special Pairs of Angles

4.1 Notes Fill in your notes. Adjacent angles share a ______________ and _______, but have no _______________________. vertexsidePoints in common.

Angle Relationships.

Warm-Up Judging by appearances, will the lines intersect? Name the plane represented by each surface of the box. the bottom 3. the top4. the front.

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

ANGLERELATIONSHIPS SECTION 1-5 and 2-8 Jim Smith JCHS Spi.3.2.E.

Section 1.5. Two angles are complementary angles if the sum of their measures is 90°. Each angle is the complement of the other. Definition of Complementary.

I CAN FIND UNKNOWN ANGLE MEASURES BY WRITING AND SOLVING EQUATIONS. 6.1 Angle Measures.

ANGLE RELATIONSHIPS Mrs. Insalaca 8 th Grade Math.

2.4 Reasoning with Properties from Algebra ?. What are we doing, & Why are we doing this?  In algebra, you did things because you were told to….  In.

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.

Section 1.6 Angle Pair Relationships standard #13 7/3/2016.

Types of Angle Pairs Foldable

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

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

Angle Relationships Lesson 1.5.

Chapter 1 section 7 Angle relationships

1.5 Exploring Angle Pairs.

Angle Relationships.

I can write and solve equations to find unknown angle measures.

Sec. 1.5: Angle Pairs There are five special pairs of angles:

1.6 Describing Pairs of Angles

Types of Angles & Their Relationships

Angle Pairs Module A1-Lesson 4

1-5 Angle Relations.

Angle Pair Relationships

Angle Relationships OBJ: To ID and use adjacent, vertical, complementary, supplementary, and linear pairs of angles, and perpendicular lines To determine.

Exploring Angle Pairs Skill 05.

Adjacent Angles Definition Two coplanar angles with a common side, a common vertex, and no common interior points. Sketch.

Proving Angles Congruent

Geometry Exploring Angle Pairs.

Presentation transcript:

PROVING ANGLES CONGRUENT

Vertical angles Two angles whose sides form two pairs of opposite rays The opposite angles in vertical angles are congruent. In this case angles 1 & 2 would be congruent and angles 3 & 4 would be congruent.

Because angles 1 & 4 form a straight line as well as angles 3 & 2 we only have to know the measure of one angle to know all of the angle If angle 3 is 60 0, then angle 2 would be because they make a straight angle of Then angle 4 would be 60 0 being vertical to angle 3 and angle 1 would be being vertical to angle

Adjacent angles Two coplanar angles with a common side, a common vertex, and no common interior points In other words, two angles share one of the same rays

Complementary angles Two angles whose measures have the sum of 90 0 Each angle is called the complement of the other As you can see from the figures the two angles can be adjacent or they can be separated but the angles must add up to 90 0

Supplementary angles Two angles whose measures have the sum of Each angle is called the supplement of the other Here again, they can be adjacent or they may be two separate angles but their measure will be

Identifying Angle Pairs Name a set of complementary angles < 2 and < 3 A set of supplementary angles < 4 and < 5 < 3 and < 4 Vertical angles < 3 and < 5

AE F B C D Name the adjacent angles: If m<EFD = 27, what is the m<AFD 180 – 27 = 153

AE B C D Conclusions you can draw from the diagram Adjacent angles Adjacent supplementary angles Vertical angles F

AE B C D F Things you cannot assume Angles or segments that are congruent If an angle is a right angle Lines are parallel or perpendicular We can assume these if there are markings

What can you conclude from this diagram? <1 and <2 Congruent <2 and <3 Adjacent <4 and <5 adjacent supplementary angles <1 and <4 vertical angles T P Q V W What conclusions can you make here?

Assignment Page – – –