Math, asked by shopt, 1 year ago

if diagonals of a parallelogram are equal then show that it is a rectangle

Answers

Answered by NUTROLLER

Let ABCD be the given ||gm. Through D draw a diagonal extending up to B and likewise, draw another diagonal from C to A. Label their intersection point as O. Measure OA and OC We observe, OA=OC and, OB=OD We conclude, Diagonals of a parallelogram bisect each other. Rectangle is another type of a quadrilateral and parallelogram. Repeat the activity above and measure the diagonals. You'll conclude: Diagonals of a rectangle are equal. This is a property of a rectangle. If two of the diagonals are drawn, they (of course) bisect each other and they ARE also equal. Hence, If diagonals of a parallelogram are equal, it is indeed a rectangle.

shopt: i cant understand what is this

NUTROLLER: This is kind of like a "comparison of properties among two shapes". It shows the similarities between a ||gm and rectangle in order to prove the above property.

NUTROLLER: These questions require intellectual thinking and perceiving the information present.

Answered by johnlibron

Answer:

Any parallelogram must be with one angle 90°.

Step-by-step explanation:

Given: Let PQRS be a parallelogram where PR = QS.

To prove: PQRS is a rectangle.

Proof: Rectangle is a parallelogram with one angle 90°. We prove that one of its interior angles is 90°.

In △PQR and △SRQ,

PQ = SR

QR = QR

PR = SQ

∴ △PQR ≅ △SRQ [SSS Congruence Rule]

→ ∠PQR = ∠SRQ [c.p.c.t.]

Now,

PQ || SR and QR is a transversal.

∴ ∠Q + ∠R = 180°

→ ∠Q + ∠Q = 180°

→ 2∠Q = 180°

→ ∠Q = 90°

So, PQRS is a parallelogram with one angle 90°.

∴ ABCD is a parallelogram.

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