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Name
Class
2-6
Date
Practice (continued)
Form G
Proving Angles Congruent
11. Given: /5 > /2
Prove: /8 > /4
1 2
4 3
Statements
6 5
8 7
1) 9 l5 O l2
Reasons
1) Given
2) /2 > /4
2) 9 Vertical Angles are O.
3) 9 l5 O l4
3) Transitive Property of Congruence
4) 9 l8 O l5
4) Vertical Angles are >.
5) /8 > /4
5) 9 Transitive Property of Congruence
12. Complete the paragraph proof below.
A
Given: /1 and /2 are complementary
D
/2 and /3 are complementary
BD bisects /ABC
2
1
Prove: m/1 5 45
B
3
We know that
and
are complementary and /2 and /3
are complementary because these facts are given. By the
,
. Using
m/2 1 m/3 5 90. Given that BD bisects /ABC, it follows that
substitution,
, or 2(m/3) 5 90. Using the
, m/3 5 45. By the
Congruent Complements Theorem,
. It follows that
, because
congruent angles have the same measure and
by substitution.
l1; l2; definition of complementary angles; ml2 5 ml3; ml3 1 ml3 5 90;
Division Property of Equality; l1 O l3; ml1 5 ml3; ml1 5 45
13. Writing Look back at the proof in Exercise 11. Rewrite the proof as a
paragraph proof.
Answers may vary. Sample: It is given that l5 O l2. Since vertical angles are O ,
it follows that l2 O l4. Using the Transitive Property of Congruence, it follows
that l5 O l4. Again, because vertical angles are O , it follows that l8 O l5.
Finally, it follows that l8 O l4, using the Transitive Property of Congruence.
Prentice Hall Gold Geometry • Teaching Resources
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