1.5 Exploring Angle Pairs 9/20/10

Slides:



Advertisements
Similar presentations
2-5 Proving Angles Congruent
Advertisements

Proving Angles Congruent.  Vertical Angles: Two angles whose sides form two pairs of opposite rays; form two pairs of congruent angles
Proving Angles Congruent
a location in space that has no size.
1-5: Exploring Angle Pairs
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?
2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.
DEFINITIONS, POSTULATES, AND PROPERTIES Review HEY REMEMBER ME!!!!!!
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.
Section 1.6 Pairs of Angles
2.3 Complementary and Supplementary Angles
SOLUTION EXAMPLE 4 Identify angle pairs To find vertical angles, look or angles formed by intersecting lines. To find linear pairs, look for adjacent angles.
1.5 Describe Angle Pair Relationships
Angle Pair Relationships
Warm Up.
Pre-AP Bellwork 6) Claire draws an angle that measures 56. Justin draws a congruent angle. Justin says his angle is obtuse. Is he correct? Why or why not?
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.
2.4 Vertical Angles. Vertical Angles: Two angles are vertical if they are not adjacent and their sides are formed by two intersecting lines.
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?
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.
1-5 Exploring Angle Pairs. Problem 1: Identifying Angle Pairs Use the diagram provided. Is the statement true? Explain.
Section 1-5: Exploring Angle Pairs Objectives: Identify special angle pairs & use their relationships to find angle measures.
Two angles are adjacent if they share a common vertex and side, but have no common interior points. SIDE BY SIDE…shoulder to shoulder. YES NO.
Proving Angles Congruent
Measuring Angles. Geometry vs Algebra Segments are Congruent –Symbol [  ] –AB  CD –  1   2 Lengths of segments are equal. –Symbol [ = ] –AB = CD.
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.
PROVING ANGLES CONGRUENT. Vertical angles Two angles whose sides form two pairs of opposite rays The opposite angles in vertical angles are congruent.
1.5 Exploring Angle Pairs.
2-4 Special Pairs of Angles Objectives -Supplementary Angles Complementary Angles -Vertical angles.
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.
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.
Honors Geometry Section 1.3 part2 Special Angle Pairs.
OBJECTIVES: 1) TO IDENTIFY ANGLE PAIRS 2) TO PROVE AND APPLY THEOREMS ABOUT ANGLES 2-5 Proving Angles Congruent M11.B C.
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.
CHAPTER 1: Tools of Geometry Section 1-6: Measuring Angles.
Exploring Angle Pairs UNIT 1 LESSON 5.
1-5 Angle Relationships Students will learn how to identify and use special pairs of angles, namely, supplementary, complementary, and congruent (have.
ANGLERELATIONSHIPS SECTION 1-5 and 2-8 Jim Smith JCHS Spi.3.2.E.
Pairs of Angles Geometry Farris O I can identify adjacent, vertical, complementary, and supplementary angles. I can find measures of pairs of angles.
2.3 Complementary and Supplementary Angles. Complementary Angles: Two angles are complementary if the sum of their measures is Complement: The sum.
1.5 Ms. Verdino. Adjacent angles are two coplanar angles with a common side, a common vertex, and no common interior points. Vertical angles are two angles.
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.
Warm up # Exploring Angles Adjacent Angles  Angles with a common vertex and one common side  Think: side by side or right next to Angles.
Angle Pair Relationships and Angle Bisectors. If B is between A and C, then + = AC. Segment Addition Postulate AB BC.
1-4: Measuring Angles.
Warm Up Solve..
Angle Pairs More Angle Pairs Definitions Pictures Angles
1.5 Exploring Angle Pairs.
Angle Relationships.
Describe Angle Pair Relationships
Angle Pairs Module A1-Lesson 4
Angles and Bisectors.
Angle Pair Relationships
Exploring Angles and Angle Relationships
Describe Angle Pair Relations
2.6 Deductive Reasoning GEOMETRY.
Exploring Angle Pairs Skill 05.
Adjacent Angles Definition Two coplanar angles with a common side, a common vertex, and no common interior points. Sketch.
Identifying Angle Pair Relationships
Geometry Exploring Angle Pairs.
Presentation transcript:

1.5 Exploring Angle Pairs 9/20/10 Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles

Adjacent Angles Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points.

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

Complementary Angles Complementary angles – two angles whose measures have a sum of 90°. Each angle is called the complement of the other.

Supplementary Angles Supplementary angles – two angles whose measures have a sum of 180°. Each angle is called the supplement of the other.

Identifying Angle Pairs Use the diagram. Is the statement true? Explain. a. are adjacent angles. b. are vertical angles. c. are complementary.

Identifying Angle Pairs No, they are not adjacent. They have a common side and common vertex, but they also have common interior points. No, they are not vertical angles. Ray FA and ray FD are opposite rays, but ray FE and ray FB are not. Yes, they are complementary. 62 + 28 = 90°.

Linear Pairs A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. The angles of a linear pair form a straight angle. Postulate 1.9 Linear Pair Postulate If two angles form a linear pair, then they are supplementary.

Finding Missing Angle Measures are a linear pair. What are the measures of ?

Finding Missing Angle Measures

Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles. Its endpoint is at the angle vertex. Within the ray, a segment with the same endpoint is also an angle bisector. The ray or segment bisects the angle.

Using an Angle Bisector to Find Angle Measures bisects . If , what is

More Practice!!!!! Classwork – Textbook p. 38 # 7 – 25 odd. Homework – Textbook p. 38 # 8 – 26 even.