GEOMETRY CHAPTER 1 1-4: Measure and Classify Angles WARM-UP Solve each equation 1.) 2.)
3.) MEASURE AND CLASSIFY ANGLES Objective: Students will be able to name, classify, and measure angles using postulates and a protractor. Agenda Vocabulary Protractor Postulate Measuring and Classifying Angles Angle Addition Postulate Finding Angle Measures
ANGLE AN INTRODUCTION An Angle consists of two different rays with the same endpoint. The rays that form the angle are known as the sides. The endpoint that connects the rays is known as the vertex. The angle with sides and can be named , , or C Verte x A
Sides B NAME ANGLES EX. 1 (PG 24 IN THE TEXTBOOK) Name the three angles in the diagram. Solution: W Y X
Z MEASURING ANGLES The Protractor Postulate: The measure of is equal to the absolute value of the difference between the real numbers for and . Notation: Example:
CLASSIFYING ANGLES Angles can be classified into one of the four following names: Acute: Less than in measure () Obtuse: Greater than , but less than in measure ()
Right : Always in measure () Straight: Always in measure () MEASURING AND CLASSIFY ANGLES Use the diagram (pg. 24) to find the measure of the indicated angle. Then classify the angle.
a.) ; Acute Angle b.) ; Obtuse Angle c.) ; Straight
Angle d.) ; Right Angle ANGLE ADDITION The Angle Addition Postulate: If is the interior of , then
FIND ANGLE MEASURES EXAMPLE 3 (PG 26) Given that , find and Solution: Because M is in the interior of , we can use the Angle Addition Postulate to first solve for x: FIND ANGLE MEASURES EXAMPLE 3 (PG 26) Next, plug in for and .
For : For : Thus, and CONGRUENT ANGLES Congruent Angles: Angles that have the same
measure Symbol: means is Congruent to IDENTIFY CONGRUENT ANGLES EXAMPLE 4 Identify the congruent angles in the diagram on page 27 in your textbook. There are two pairs of congruent angles: And BISECTING AN ANGLE Angle bisector: A ray that divides the angle into two angles
that are congruent. In the diagram, bisects . A So, D And B
C EXAMPLE 5 (PG. 28 IN YOUR TEXTBOOK) In the diagram at the right, bisects , and , Find Solution: Because bisect , then X And with the Angle Addition Postulate
W Y Z HOMEWORK 1-4 Pg. 28-30 #s 3, 6, 11-14, 15-20, 23, 25, 26, 29-31, 33- 38, 40, 41 44-47 (EC)