Question

prove that the quadrilateral formed by joining the angle bisectors of interior angles of a parallelogram is a rectangle...​

Answer 1

Answer:

To prove Quadrilateral PQRS is a rectangle. Proof Since, ABCD is a parallelogram, then DC || AB and DA is a transversal. Thus, PQRS is a quadrilateral whose each angle is 90°. Hence, PQRS is a rectangle.

Step-by-step explanation:

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Answer 2

Answer:

$\large\green{\textsf{✩ Verified Answer ✓}}$

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$\huge{\textsf{Given :}}$

ABCD a parallelogram

$\huge{\textsf{To Prove : }}$

PQRS is a rectangle

DC ∣∣ AB and DA is a traversal

∴ ∠A+∠D=18$0^{0}$

$\frac{1}{2}$ ∠A + $\frac{1}{2}$ ∠D = $90^{0}$

⇒∠SAD + ∠SDA = $90^{0}$

∴ ∠ASD = $90^{0}$

∴ By concept of vertical angles

∠ASD = ∠PSR = $90^{0}$

Simillarly we will get

∠PQR = ∠QPS = ∠QRS = $90^{0}$

∴ PQRS is a rectangle

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$\bf\pink{\textsf{Answered By ❥Princess࿐ }}$