Question

In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and segment DF is congruent to segment BD . Point C is the point of intersection between segment AG and segment BD while point E is the point of intersection between segment AG and segment DF .

Prove ΔABC ≅ ΔGFE. (10 points)

Answer 1

Explanation:

Given:

∠DCE ≅ ∠DEC

∠B ≅ ∠F

DF ≅ BD

To prove:

ΔABC ≅ ΔGFE

Solution:

Statements Reasons

1). ∠DCE ≅ ∠DEC 1). Given

2). ∠ACB ≅ ∠GEF 2). Vertically opposite angles to the

congruent angles.

3). ∠B ≅ ∠F 3). Given

4). DB ≅ DF 4). Given

5). DC + CB ≅ DE + EF 5). Segment addition postulate

6). DC ≅ DE 6). Property of isosceles triangle

7). CB ≅ EF 7). Transitive property

8). ΔABC ≅ ΔGFE 8). ASA property of congruence