a transversal cuts two Parallel Lines prove that bisector of interior angles form rectangle
Answers
Question: A transversal cuts two Parallel Lines prove that bisector of interior angles form rectangle
(Based on NCERT Grade 9 Mathematics)
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Pre-Requisite Knowledge
Alternate interior angles are equal.
Sum on co-interior angles is equal to 180°
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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.
Since they bisect each other at 90°, it is a rectangle.
(figure attached to refer)
Answer:
Step-by-step explanation:
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.
Since they bisect each other at 90°, it is a rectangle.
