Question

WILL GIVE BRAINIEST AND POINTS :

In a parallelogram ABCD, the lengths of the sides AD and AB are 8 in and 3 in respectively. Angle bisectors of ∠A and ∠D split the opposite side into three segments. Find the length of each of these segments.

Answer 1

Answer:

BE = FC = 3 inches, EF = 2 inches

Step-by-step explanation:

The sum of angles A and D is 180°, so the sum of their half-angles is 90°. That is, half of A plus half of B add to 90°, so the bisector from B intersects AE at a right angle. Call that point of intersection X.

Then angle ABX = angle EBX, so triangle ABX is congruent to triangle EBX. Sides AB and BE are corresponding sides of congruent triangles.

The same argument applies to sides DC and CF.

Thus we have BE = CF = 3 inches, and EF is the left-over distance, 2 inches.