Download 3-5 Reteaching

Name
Class
Date
Reteaching
3-5
Parallel Lines and Triangles
Triangle Angle-Sum Theorem:
The measures of the angles in a triangle add up to 180.
In the diagram at the right, ∆ACD is a right triangle. What are
m1 and m2?
Step 1
Angle Addition Postulate
m1 + mDAB = 90
Substitution Property
m1 + 30 = 90
Subtraction Property of Equality
m1 = 60
Step 2
Triangle Angle-Sum Theorem
m1 + m2 + mABC = 180
Substitution Property
60 + m2 + 60 = 180
Addition Property of Equality
m2 + 120 = 180
Subtraction Property of Equality
m2 = 60
Exercises
Find m1.
1.
2.
3.
4.
5.
6.
Algebra Find the value of each variable.
7.
8.
9.
Prentice Hall Geometry • Teaching Resources
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Name
Class
Date
Reteaching (continued)
3-5
Parallel Lines and Triangles
In the diagram at the right, 1 is an exterior angle of the triangle. An
exterior angle is an angle formed by one side of a polygon and an
extension of an adjacent side.
For each exterior angle of a triangle, the two interior angles that are not next to it
are its remote interior angles. In the diagram, 2 and 3 are remote interior angles
to 1.
The Exterior Angle Theorem states that the measure of an exterior angle is equal to the
sum of its remote interior angles. So, m1 = m2 + m3.
What are the measures of the unknown angles?
Triangle Angle-Sum Theorem
mABD + mBDA + mBAD = 180
Substitution Property
45 + m1 + 31 = 180
Subtraction Property of Equality
m1 = 104
Exterior Angle Theorem
mABD + mBAD = m2
Substitution Property
45 + 31 = m2
Subtraction Property of Equality
76 = m2
Exercises
What are the exterior angle and the remote interior angles for each triangle?
10.
11.
12.
exterior:
exterior:
exterior:
interior:
interior:
interior:
Find the measure of the exterior angle.
13.
14.
15.
Prentice Hall Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
50