Question

Prove that Corresponding angles formed by a transversal of the two parallel lines are of Equal Measure..​

Answer 1

Step-by-step explanation:

Theorem:

If a pair of corresponding angles formed by a transversal of two lines is congruent then the two lines are parallel

[ Note : or you can also write this theorem which you mention in the question :-Corresponding angles formed by a transversal of the two parallel lines are of Equal Measure..]

Given :

Line n is a transversal of line l and line m. ∠a and ∠b is a congruent pair of corresponding angles. That is ∠a= ∠b.

To prove :

line l || line m

Proof:

∠a + ∠c= 180° ..... (Angles in a linear pair)

∠a = ∠b ... (Given)

therefore, ∠b + ∠s= 180°

That is the interior angles on the same side of the transversal are supplementary

therefore, line l || line m ...( Interior angles test)

hence proved

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[ Note:- This property is called the corresponding angles test of parallel lines.]

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hope it helps....