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

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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
$In Δ A P B and Δ C Q D, A B = C D (opposite sides of a parallelogram) . ∠ A B P = ∠ C D Q (alternate angles) . ∠ A P B = ∠ C Q D (both are right angles) . ∴ Δ A P B ≅ Δ C Q D (using A.A.S. criterion) . Hence, statement 1 is correct but statement 2 is false.$

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Similar questions

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

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

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

Pick the correct option.

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

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Is it necessary to have a 90° angle in rhs congruence rule or by having equal hypotenuse and equal side we can apply RHS congruence rule?

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In parallelogram ABCD,AP and CQ are perpendicular to diagonal BD.Statement 1:ΔAPB≅ΔCQD,Statement 2: RHS congruence is applied Pick the correct option.

The correct option is C Statement 1 is correct but 2 is falseIn ΔAPB and ΔCQD,AB=CD (opposite sides of a parallelogram).∠ABP=∠CDQ (alternate angles).∠APB=∠CQD (both are right angles).∴ΔAPB≅ΔCQD (using A.A.S. criterion).Hence, statement 1 is correct but statement 2 is false.

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

Pick the correct option.