prove the triangles congruent when statements on left side are true using theorems such as asa, if not congruent write no congruence

Question

Answer 1

It is congruent for 1., in parallelogram diagonal makes two congruent triangles. there are logic steps to prove it including assumption implies equal sides. Something like two parallel lines cut by two parallel lines creates equal opposite sides. The diagonal is a shared side. So tringles congruent SSS

#2. same kind of as 1. and then SSS

#3. might not be a parallelogram (a non isosceles trapezoid) and triangle cannot be proven congruent.

#4 makes sure the quadrilateral is rectangle and you can prove triangle congruent.

again A rectangle has equal opposite sides. SSS

#5 does not lead to congruent triangles because the given implies two isosceles triangles but not that they are equal isosceles

Answer 2

No, the triangels cannot be proven to be congruent. Nothing is given as to the characteristics of ABCD.