Skills Practice Workbook - Glencoe

15–4
Complete each proof.
1. If m�1 � m�2 and m�3 � m�4, then
m�ABC � m�ROD.
R 2
Given: m�1 � m�2, m�3 � m�4
Prove: m�ABC � m�ROD
A
O
Proof:
1
3
Statements Reasons
B C
a. m�1 � m�2, m�3 � m�4 a. Given
b. m�ABC � m�1 � m�3
m�ROD � m�2 � m�4
b. Angle Addition Postulate
c. m�1 � m�3 � m�2 � m�4 c. Addition Property of Equality
d. m�ABC � m�ROD d. Substitution Property of Equality
4
7x
�
6
2. If � 14, then x � 12.
7x
�
6
Given: � 14
NAME DATE PERIOD
Skills Practice
Preparing for Two-Column Proofs
Prove: x � 12
Proof:
Statements Reasons
7x
a. �� � 14 a. Given
6
b. 7x � 84 b. Multiplication Property of Equality
c. x � 12 c. Division Property of Equality
3. If �ABC is a right triangle with �C a right
angle and m�A � m�B, then m�A � 45.
Given: �ABC is a right triangle with �C a
right angle and m�A � m�B.
Prove: m�A � 45
A
Proof:
C B
Statements Reasons
a. �ABC is a right triangle with �C a a. Given
right angle and m�A � m�B
b. m�A � m�B � m�C � 180 b. Angle Sum Theorem
c. m�C � 90 c. Definition of Right Angle
d. m�A � m�B � 90 d. Subtraction Property of Equality
e. m�A � m�A � 90 e. Substitution Property of Equality
f. 2m�A � 90 f. Substitution Property of Equality
g. m�A � 45 g. Division Property of Equality
© Glencoe/McGraw-Hill 88 Geometry: Concepts and Applications
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