Question

AB and CD are parallel lines and a trasversal L intesects AB at X and CD at Y . Prive that the bisectors of the interior angles bisect each ither and froms a rectangle.


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Answer 1

hey mate
here's the proof

Answer 2

Ello There!

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Question: If two parallel lines are intersected by a transversal , prove that the bisector of interior angles on the same side of transversal intersect each other at right angles.

(Based on NCERT Grade 9 Mathematics)

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Pre-Requisite Knowledge

• Alternate interior angles are equal.

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Answer

Given,

Interior angles on the same side of the transversal are bisected.

To Prove,

∠XSY = 90°

∠XQY = 90°

Proof,

∠BXY + ∠DYX = 180° (co-interior angles)

∠BXY + ∠DYX = 180° (halves of equals are equal)

∠1 + ∠2 = 90°   →1

Now,

In Δ XQY

∠1 + ∠2 + ∠XQY = 180° (A.S.P of triangles)

90° + ∠XQY = 180° (From →1)

        ∠XQY = 180° - 90°

        ∠XQY = 90°     →2

Similarly we can prove that,

          ∠XSY = 90°   →3

From 2 and 3,  Interior angles on the same side of transversal intersect each other at right angles.

(figure attached to refer)

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Hope It Helps!