In Fig. 4.143, ∠A = ∠CED, prove that Δ CAB ∼ Δ CED. Also, find the value of x.

Given: ∠A = ∠CED

To prove: Δ CAB ∼ Δ CED

To find: The value of x.

Theorem Used:

If two triangles are similar, then the ratio of their corresponding sides are equal.

Explanation:

We have, ∠A = ∠CED

In ΔCAB and ΔCED

∠C = ∠C (Common)

∠A = ∠CED (Given)

Then, ΔCAB ~ ΔCED (By AA similarity)

As corresponding parts of similar triangle are proportional.

So,

Substituting the given values, we get,

⇒ 15x = 90

⇒ x = 90/15

⇒ x = 6cm