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Mathematics

Assertion (A): Using the information in the given figure, we get : ∠PQR = ∠PSR = 90°

Using the information in the given figure, we get : ∠PQR = ∠PSR = 90°. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

Reason (R):

Using the information in the given figure, we get : ∠PQR = ∠PSR = 90°. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

By SSS, △PQR = △PSR
⇒ ∠PQR = ∠PSR
Since, ∠PQR + ∠PSR ≠ 180°
∴ ∠PQR = ∠PSR ≠ 90°

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Triangles

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Answer

A is false, R is true.

Explanation

Given,

Join PR.

Using the information in the given figure, we get : ∠PQR = ∠PSR = 90°. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

In △PQR and △PSR,

PR (Common side)

PQ = PS (Given)

QR = RS (Given)

∴ △PQR ≅ △PSR (By SSS)

By C.P.C.T.C.

∠PQR = ∠PSR
∠RPQ = ∠RPS
∠PRQ = ∠PRS

Assuming, ∠PQR = ∠PSR = 90°

⇒ ∠QPS = QRS = 90° [∵ Sum of interior ∠s of quadrilateral is 360°]

So, PQRS should be a rectangle with all it's angles equal to 90°.

But PQRS is not a rectangle as opposite sides are not equal.

PS ≠ QR and PQ ≠ SR

Hence our assumption ∠PQR = ∠PSR = 90° is incorrect.

∴ ∠PQR = ∠PSR ≠ 90°

∴ Assertion (A) is false.

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.

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