Question

Answer plz question 57

Answer 1

Question :

In the given figure, if ∠AED = ∠BDC + ∠BAE, then show that AB || CD.

Step-by-step explanation:

Given : ∠AED = ∠BDC + ∠BAE

To Prove : AB || CD

Proof : In ∆ ABE, ∠AED is an exterior angle

∴ ∠AED = ∠BAE + ∠ABE ...(i)

(Exterior angle theorem)

But,

∠AED = ∠BDC + ∠BAE ...(ii)

From (i) and (ii), we get

∠BAE + ∠ABE = ∠BDC + ∠BAE

∠ABE = ∠BDC

Also, from the figure, we can conclude that ∠ABE and ∠BDC are alternate interior angles and BD acts as a transversal line.

∴ AB || CD

Hence, proved !!

Theorem used :

• Exterior angle sum theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of two non-adjacent interior angles of a triangle.