In figure 9.38, AE bisects ∠CAD and ∠B = ∠C. Prove that AE ∥ BC.

Question:

In figure 9.38, AE bisects ∠CAD and ∠B = ∠C. Prove that AE ∥ BC.

Solution:

Let ∠B = ∠C = x

Then,

∠CAD = ∠B + ∠C = 2x (exterior angle)

⇒1/2∠CAD = x

⇒ ∠EAC = x

⇒ ∠EAC = ∠C

These are alternate interior angles for the lines AE and BC

∴ AE ∥ BC

Leave a comment

None
Free Study Material