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Problem 1

We have two possible answers here.

Either AC = DF is needed, or AB = DE is needed

We can't use BC = EF, as that would be ASA. The sides cannot be between the marked angles. With AAS, the sides are not between the angles.

Note: AC pairs up with DF because both segments have an endpoint at an angle with one arc marking. AB pairs up with DE because one endpoint has a double arc marking.

Problem 2

We have a pair of congruent sides (due to the tickmarks) and a pair of congruent angles. We need another pair of angles. We can't pick angle B = angle E, as that would give us ASA. So we must pick the other pair of angles

angle A = angle D

If angle A = angle D, then we have enough to use AAS.

tangent

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc