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Byju's Answer

Standard VIII

Mathematics

AAS Postulate

In parallelog...

Question

In parallelogram ABCD, AP and CQ are perpendicular to diagonal BD.
It can be proved that $Δ$ APB $≅$ $Δ$ CQD.

True

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False

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Solution

The correct option is A
True

In $Δ$ APB and $Δ$ CQD,

AB=CD Opposite sides of a parallelogram

$∠$ ABP= $∠$ CDQ

Alternate angles

$∠$ APB = $∠$ CQD both are right angles

$∴$ $Δ$ APB $≅$ $Δ$ CQD using AAS criterion

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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

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

(i) ΔAPB ≅ ΔCQD

(ii) AP = CQ

P

and

Q

are the points of trisection of the diagonal

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of a parallelogram

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. Prove that

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is parallel to

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A B C D

is a parallelogram and

A P

and

C Q

are perpendiculars from vertices

A

and

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on diagonal

B D

.Show that

A P = C Q

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?

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In parallelogram ABCD, AP and CQ are perpendicular to diagonal BD. It can be proved that ΔAPB ≅ ΔCQD.

The correct option is A True In ΔAPB and ΔCQD, AB=CD Opposite sides of a parallelogram ∠ ABP=∠ CDQ Alternate angles ∠APB = ∠CQD both are right angles ∴ Δ APB ≅ Δ CQD using AAS criterion

In parallelogram ABCD, AP and CQ are perpendicular to diagonal BD.
It can be proved that $Δ$ APB $≅$ $Δ$ CQD.

The correct option is A
True

In $Δ$ APB and $Δ$ CQD,

AB=CD Opposite sides of a parallelogram

$∠$ ABP= $∠$ CDQ

Alternate angles

$∠$ APB = $∠$ CQD both are right angles

$∴$ $Δ$ APB $≅$ $Δ$ CQD using AAS criterion