Question

PLZ HELP!

Complete this proof.
Given: a | | b
Prove: ΔMOP ~ ΔRON

Answer 1

As shown in the given figure

line a // line b ⇒ given

MR and NP are transversals

So, for ΔMOP and ΔRON, we can conclude the following

(1) ∠1 = ∠2 ⇒⇒⇒ alternative angles are congruent

(2) ∠ MOP = ∠ RON ⇒⇒⇒ vertical angles are congruent

(3) ∠ 4 = ∠ 3 ⇒⇒⇒ alternative angles are congruent

So, from 1,2 and 3

∴ ΔMOP ~ ΔRON by AAA-Rule

Answer 2

As shown in the given figure
line a // line b ⇒ given
MR and NP are transversals
So, for ΔMOP and ΔRON , we can conclude the following
(1) ∠1 = ∠2 ⇒⇒⇒ alternative angles are congruent
(2) ∠ MOP = ∠ RON ⇒⇒⇒ vertical angles are congruent
(3) ∠ 4 = ∠ 3 ⇒⇒⇒ alternative angles are congruent

So, from 1,2 and 3
∴ ΔMOP ~ ΔRON by AAA-Rule