LESSON
1.4
NAME _________________________________________________________ DATE ____________
Reteaching with Practice For use with pages 26–32
GOAL
Use angle postulates and classify angles as acute, right, obtuse, or straight VOCABULARY An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle. Angles that have the same measure are called congruent angles. A point is in the interior of an angle if it is between points that lie on each side of the angle. A point is in the exterior of an angle if it is not on the angle or in its interior. An acute angle has measure greater than 0 and less than 90. A right angle has measure equal to 90. An obtuse angle has measure greater than 90 and less than 180. A straight angle has measure equal to 180. Two angles are adjacent angles if they share a common vertex and side, but have no common interior points. Postulate 3 Protractor Postulate:→ → Consider a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180. The measure of AOB is equal to the absolute value of the difference → → between the real numbers for OA and OB. Postulate 4 Angle Addition Postulate: If P is in the interior of RST, then mRSP mPST mRST.
EXAMPLE 1
Naming Angles
Lesson 1.4
Write three names for the angle and name the vertex and sides of the angle.
O N
P
SOLUTION NOP, PON, and O are all appropriate names for this angle. → → The vertex of this angle is point O and the sides are ON and OP. 56
Geometry Chapter 1 Resource Book
Copyright © McDougal Littell Inc. All rights reserved.
LESSON
1.4
CONTINUED
NAME _________________________________________________________ DATE ____________
Reteaching with Practice For use with pages 26–32
Exercises for Example 1 Write three names for the angles and name the vertex and sides of each. 1.
2.
3.
C
D
G H
E
B A
I F
EXAMPLE 2
Classifying Angles in a Coordinate Plane Plot the points A1, 1, B1, 1, C1, 3, D3, 2, and E3, 1. Then classify the following angles as acute, right, obtuse, or straight. a. CAB b. DAE c. BAD d. EAB SOLUTION Begin by plotting the points, then observe whether each angle is less than 90, equal to 90, between 90 and 180, or equal to 180. a. right angle b. acute angle c. obtuse angle
y
C(1, 3) B(1, 1)
2
D(3, 2) E(3, 1)
d. straight angle
x
1 A(1, 1)
Exercises for Example 2 Plot the given points and classify the given angles as acute, right, obtuse, or straight. 4. A2, 4, B5, 1, C0, 0, and
D3, 0
5. E4, 0, F3, 2, G1, 0, H1, 2,
I1, 2
a. HGF
b. BCD
b. EGF
c. ACD
c. EGI
Lesson 1.4
a. ACB
d. FGI e. HGI
Copyright © McDougal Littell Inc. All rights reserved.
Geometry Chapter 1 Resource Book
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