1-4: Measuring Angles.

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Presentation transcript:

1-4: Measuring Angles

Parts of an Angle Formed by the union of two rays with the same endpoint. Called sides of the angle Called the vertex of the angle 3 ways to name BAC or CAB A (Vertex) 1 Exterior A B Interior 1 C

Types of Angles Congruent Angles Angles with the same measure Acute Right Obtuse Straight Congruent Angles Angles with the same measure

Example 1: 1). Name the angle below. Name the sides and the vertex of the angle. X Y Z 1 2). Label the 3 points on the figure below so that the angle has sides KQ and KN. Q K N

Protractor Postulate Consider and a point on one side of . Every ray of the form can be paired one to one with a real number 0 to 180. A B O

135° 45° A D a d Example 2: What is ?

Postulate 1-8: Angle Addition Postulate If point B is in the interior of , then: Example 3: If , what are and ?

Classwork: p. 31 #’s 6, 7, 12-14, 18, 20, 22, 23, 29-31

1-5: Exploring Angle Pairs

Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles Two coplanar angles with a: _______________, ________________, _______________________________ common side common vertex no common interior points Two angles whose sides are __________ ______ opposite rays Two angles whose measures have a sum of _______ Two angles whose measures have a sum of _______

Example 1: Use the diagram below. Is each statement true? Explain. and are adjacent angles. and are vertical angles. and are supplementary. Yes, they have a common side No, they don’t share two pairs of opposite rays Yes, the sum of the angles is 180°

Assumptions About Angles Assumptions you can make: Angles are adjacent Angles are adjacent and supplementary Angles are vertical angles Assumptions you can’t make: Angles or segments are congruent An angle is a right angle Angles are complementary

Postulate 1-9: Linear Pair Postulate A Linear Pair of angles are angles that are both supplementary and adjacent. Ex 2 What are the measures of and ?

Theorem 2-1: Vertical Angle Theorem Vertical angles are congruent and Example 3: What is the value of x? What are the angle measures?

Angle Bisector A ________ which divides an angle into ______ _______________ angles. ray two congruent is an angle bisector. Example 4: bisects . If , what is ?

Homework: p. 38 # 7-23 odd, 26-32 even