In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

The length of AC = 18 meters.

Step-by-step explanation:

Given : ∠ABC ≅ ∠ACD, BC = 12 m and AD = 27 m

To find : AC

Solution : Since, the bases of the trapezoid are parallel to each other

⇒ AD ║ BC

So, ∠ACB = ∠CAD ( Alternate interior angles are equal)

Now, in ΔACB and ΔDAC,

∠ABC ≅ ∠ACD (Given)

∠ACB = ∠DAC (Proved above)

So, BY AA postulate of similarity of triangles, ΔACB ~ ΔDAC

Since, the sides of similar triangles are proportion to each other

Hence, the length of AC = 18 meters.