Question

abcd is a parallelogram.if the line joining the mid-point of side bc to vertex a bisects angle a,then prove that bisector of angle b also bisects ad​

Answer 1

let M and N be where these angle bisectors meet BC and AD,
Let E be the point where they intersect each other.
Since consecutive angles of a parallelogram are supplementary, their bisectors are complementary. Thus, triangles ABE and ANE are right triangles, and by AAA they are similar. Since they share side AE, they are congruent. Thus, AN ≅ BM and BN bisects AD.