Chapter: Similarity· Mathematics Part 2 (Geometry)

Asked in: July 2024 board paperIn \(\Delta ABC\) and \(\Delta PQR\), in a one to one correspondence of vertices, \(\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}\), then ____ statement is true.[Figure: a small triangle ABC with A at the top left, B…

Asked in: July 2024 board paper

In \(\Delta ABC\) and \(\Delta PQR\), in a one to one correspondence of vertices, \(\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}\), then ____ statement is true.

[Figure: a small triangle ABC with A at the top left, B below it and C to the right of B; a larger similarly shaped triangle with Q at the top, R below Q and P to the right of R, so that A corresponds to Q, B to R and C to P.]

A. \(\Delta PQR \sim \Delta ABC\)

B. \(\Delta PQR \sim \Delta CAB\)

C. \(\Delta CBA \sim \Delta PQR\)

D. \(\Delta BCA \sim \Delta PQR\)

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: (B) \(\Delta PQR \sim \Delta CAB\)

Read the correspondence from the equal ratios: \(\dfrac{AB}{QR}\) pairs A with Q and B with R; \(\dfrac{BC}{PR}\) pairs B with R and C with P; \(\dfrac{CA}{PQ}\) pairs C with P and A with Q.

So A ↔ Q, B ↔ R, C ↔ P, and \(\Delta ABC \sim \Delta QRP\) (SSS test of similarity).

Writing the same correspondence starting from P: P ↔ C, Q ↔ A, R ↔ B, i.e. \(\Delta PQR \sim \Delta CAB\). The other options pair the vertices wrongly.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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Asked in: July 2024 board paperIn \(\Delta ABC\) and \(\Delta PQR\), in a one to one correspondence of vertices, \(\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}\), then ____ statement is true.[Figure: a small triangle ABC with A at the top left, B…

1 answer

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