$In parallelogram A B C D, A P and C Q are perpendicular to diagonal B D . Statement 1: Δ A P B ≅ Δ C Q D, Statement 2: SSA congruence is applied$

Pick the correct option.

Both statements are correct

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Both statements are false

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Statement 1 is correct but 2 is false

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Statement 1 is false but 2 is correct

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Solution

The correct option is C
Statement 1 is correct but 2 is false

$In Δ A P B and Δ C Q D, A B = C D (opposite sides of a parallelogram) . ∠ A B P = ∠ C D Q (alternate angles) . ∠ A P B = ∠ C Q D (both are right angles) . ∴ Δ A P B ≅ Δ C Q D (using A.A.S. criterion) .$

There is no SSA postulate for congruency.
Hence, statement 1 is correct but statement 2 is false.

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In parallelogram A B C D, A P and C Q are perpendicular to diagonal B D . Statement 1: Δ A P B ≅ Δ C Q D, Statement 2: RHS congruence is applied

In parallelogram A B C D, A P and C Q are perpendicular to diagonal B D . Statement 1: Δ A P B ≅ Δ C Q D Statement 2: SSS congruence is applied

In parallelogram A B C D, A P and C Q are perpendicular to diagonal B D . It can be proved that: Statement 1: Δ A P B ≅ Δ C Q D, Statement 2: RHS congruence is applied

Choose the correct answer in each of the following:

Which of the following is not a criterion for congruence of triangles?

(a) SSA (b) SAS (c) ASA (d) SSS

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