Question

abcd is a square and x is a mid point of AB and YIs bisector of CD prove that ADX and BCY triangles are congruent

Answer 1

AX=YC [AB=CD and x and y are midpoints respectively so AX=XB=YC=YD]
DA=CB [all sides are equal of square]
angle DAX= angle DCB [90 degree]
triangle DAX is congruent to triangle YCB
BY side angle side criteria

Answer 2

this is congruent by SAS criteria