Math, asked by manitagurjar6, 5 months ago

If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose:-Required to answer. Single choice.

(1 Point)

(a) a Square

(b) a Rectangle

(c) a Parallelogram

(d) a Trapezium

Answers

Answered by s1266aakansha782696
1

Hey mate,

Given: Two parallel lines AB and CD and a transversal EF intersect them at G and H respectively. GM, HM, GL and HL are the bisectors of the two pairs of interior angles.

To Prove: GMHL is a rectangle.

Proof:

∵AB∥CD

∴∠AGH=∠DHG (Alternate interior angles)

⇒ 21∠AGH=21∠DHG

⇒∠1=∠2

(GM & HL are bisectors of ∠AGH and ∠DHG respectively)

⇒GM∥HL

(∠1 and ∠2 from a pair of alternate interior angles and are equal)

Similarly, GL∥MH

So, GMHL is a parallelogram.

∵AB∥CD

∴∠BGH+∠DHG=180o

(Sum of interior angles on the same side of the transversal =180o )

⇒ 21∠BGH+21∠DHG=90o

⇒∠3+∠2=90o

.....(3)

(GL & HL are bisectors of ∠BGH and ∠DHG respectively).

In ΔGLH,∠2+∠3+∠L=180o

⇒90o+∠L=180 oUsing (3)

⇒∠L=180 o −90 o

⇒∠L=90 o

Thus, in parallelogram GMHL, ∠L=90o

Hence, GMHL is a rectangle.

Hope it helps.

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