Question

In the given figure, if ∠a = ∠b then prove that line l || line m.

Answer 1

Given: ∠a ≅ ∠b  

To prove: line l| line m

Proof:

consider ∠c as shown in the figure ∠a ≅ ∠c …….. (i) [Vertically opposite angles] 

But, ∠a ≅ ∠b I (ii) [Given] 

∴ ∠b ≅ ∠c [From (i) and (ii)] 

But, ∠b and ∠c are corresponding angles on lines l and m when line n is the transversal. 

∴ line l || line m. [Corresponding angles test]