PROBLEM SET #4
PROVING CONGRUENCE OF TRIANGLES
A. Fill in the blanks by choosing the correct reason below to complete the two-column proof.
a. Definition of Angle Bisector
f. VAT
b. ASA Postulate
g. Definition of a Midpoint
c. Reflexive Property of Congruence (RPC)
h. SAS Postulate
d. SSS Postulate
i. Given
e. CPCTC
E
A
Given: 𝐵 is the midpoint of ̅̅̅̅̅
AC and ̅̅̅̅
DE
Prove: ABD  CBE
B
D
STATEMENTS
C
REASONS
1) 𝐵 is the midpoint of ̅̅̅̅̅
AC and ̅̅̅̅
DE
1)
2) AB  BC
2)
3) DB  BE
3)
4) ABD  CBE
4)
5) ABD  CBE
5)
B. Complete the table below to prove the congruence of the triangles.
B
C
Given: BC  DA and BC DA
Prove: ABD  CDB
A
D
STATEMENTS
REASONS
1)
1) Given
2) BC DA
2)
3) BDA  DBC
3)
4)
4) RPC
5) ABD  CDB
5)
C. Write a two-column proof.
Given: AN  EN
MN bisects N
Prove: NMA  NME
A
M
N
(5 statements)
E
STATEMENTS
REASONS
1)
1) Given
2)
2) Given
3)
3)
4)
4)
5)
5)