Question

If (AB = DE), (CA = FD), angle B is congruent to angle E, angle A is congruent to angle D, then ∆ABC and ∆DEF are congruent by the ASA criterion. If (AB = DE), angle B is congruent to angle E, (CA = FD), angle A is congruent to angle D, then ∆ABC and ∆DEF are congruent by the SAS criterion. ∆ABC and ∆DEF are congruent if angle A is congruent to angle D, (AB = DE), (AB = DF).

A) ∆ABC, ∆DEF
B) ∆DEF, ∆ABC
C) None of the above
D) Both A and B

Answer 1

The question seeks to establish congruency between two triangles, ∆ABC and ∆DEF, but the provided conditions offer a contradiction, and we cannot determine congruency without further accurate information.

Step-by-step explanation:

The question aims to determine congruency between two triangles, ∆ABC and ∆DEF, given different conditions. When all three angles or sides of two triangles are equal, they are considered congruent. According to the given conditions, ∆ABC and ∆DEF are congruent if angle A is congruent to angle D, and two sides are equal, AB = DE and AB = DF. However, the information provided is contradictory since it states AB equals both DE and DF, which cannot be correct if DE and DF are distinct sides of ∆DEF. Therefore, without additional accurate information, we cannot conclude congruency based solely on the conditions given