In figure, if x = y and a = b, prove that r || n.

Solution

r and m are two lines and a transversal p intersects them such that
x = y
But these angles form a pair of equal corresponding angles
∴ r || m ...(1)
Again, m and n are two lines and a transversal q intersects them such that
a = b
But these angles form a pair of equal corresponding angles
∴ m || n ...(2)
From (1) and (2), we have r || n.

Some More Questions From Lines and Angles Chapter

Prove “if two lines intersect each other, then the vertically opposite angles are equal.”

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Lines And Angles

In figure, if x = y and a = b, prove that r || n.

Some More Questions From Lines and Angles Chapter

Prove “if two lines intersect each other, then the vertically opposite angles are equal.”

In figure, OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ. Show that the points A, O and B are collinear.

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