Question

1. Given: AB ≅ AD and ≅ EACA Prove: Δ ABC ≅ Δ ADE

Answer 1

Since segment AB and segment AE are congruent (given), the triangle ABE must be isoscles by definition of an isosceles triangle. 
From that it follows that angle ABC must be congruent to angle AED, again by definition of an isosceles triangle. 
Then because you are given that segment BC and segment DE are congruent, triangle ABC must be congruent to triangle AED by SAS. 
Now you aren't clear whether angle 1 is angle ACB or ACD. Assume it is ACB, then ACB is congruent to ADE by CPCT. Therefore angle 1 equals angle 2. QED. 
If angle 1 is ACD and angle 2 is ADC, then since angle ACB is supplementary to angle ACD, angle ADE is supplementary to angle ADC, and from the step above angle ACB is congruent to angle ADE, then angle ACD is congruent to angle ADC by transitive equality. Therefore angle 1 equals angle 2. QED. 

Really Hope it helps, took a long time to type : 3

Answer 2

Answer:

$\Delta ABC\cong\Delta ADE$ are congruent by SAS (Side-Angle-Side) postulate.

Step-by-step explanation:

We have been given a diagram. We are asked to prove that triangle ABC is congruent to triangle ADE.

We have been given that segment AB is congruent to segment AD and segment EA is congruent to segment CA.

We can see that angle BAC and angle DAE are vertical angle, so their measures will be equal.

Since the two sides of triangle BAC (CA and AB) and included angle BAC is equal to two sides of triangle DAE (EA and AD) and included angle DAE, therefore, both angles are congruent by SAS (Side-Angle-Side) postulate.