In trapezoid ABCD, angles ABC and ACD are equal. Find the AC diagonal. if the bases ВС

In trapezoid ABCD, angles ABC and ACD are equal. Find the AC diagonal. if the bases ВС and АD are respectively equal to 24 cm and 54 cm …

Let us prove that triangles ABC and ACD are similar.

The angle ABC of the triangle ABC, by condition, is equal to the angle ACD of the triangle ACD.

The angle ACB of the triangle ABC is equal to the angle CAD of the triangle ACD as criss-crossing angles at the intersection of parallel lines AD and BC secant AC.

Then triangles ABC and ACD are similar in two angles.

Then AC / AD = BC / AC.

AC / 54 = 24 / AC.

AC ^ 2 = 54 * 24 = 1296.

AC = √1296 = 36 cm.

Answer: AC = 36 cm.