Question

Given the figure shown to the

right, write a two-column proof to
prove ZCAE ZCEA
1. Z
Statements
BC
2. ΔΑΒC ~ ΔΕDC
4. A
3. AC EC
ZABC
is isosceles
5. ZCAE CEA
1. Given
2.
B
5.
Reasons
3.
4. Definition of isosceles
VE
a

Answer 1

The prove, angle CAE is congruent to angle CEA. is achieved using AAS congruence theorem and Isosceles triangle theorem

How to complete the proof

The two column proof is written as follows

Statement Reason

∠ BAC ≅ ∠ DEC given

∠ ABC ≅ ∠ EDC given

BC ≅ DC given

Δ ABC ≅ Δ ΕDC AAS congruence theorem

Δ ACE Definition of isosceles

∠ CAE ≅ ∠ CEA Base angles of Isosceles triangle are congruent