In the following diagram- AP and BQ are equal and parallel to each other- Prove that - i - AOP - BOQ- ii AB and PQ bisect each other-

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Standard IX

Mathematics

AAS Criteria for Congruency

In the follow...

Question

In the following diagram, AP and BQ are equal and parallel to each other.

Prove that :

(i) $Δ$ AOP $≅ Δ$ BOQ.

(ii) AB and PQ bisect each other.

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Solution

In $△ A O P a n d △ B O Q$

AP=BQ (given)
$∠ O A P = ∠ O B Q (e a c h 90^{0}$
$∠ A O P = ∠ B O Q$ (vertically opposite angle)

$△ A O P i s ≅ △ B O Q$ (by AAS rule)

By CPCT
OP=OQ
AO=OB
Hence proved

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In the following diagram, AP and BQ are equal and parallel to each other. Prove that : (i) Δ AOP ≅Δ BOQ. (ii) AB and PQ bisect each other.

In △AOPand△BOQ AP=BQ (given) ∠OAP=∠OBQ(each900 ∠AOP=∠BOQ(vertically opposite angle) △AOPis≅△BOQ (by AAS rule) By CPCT OP=OQ AO=OB Hence proved

In the following diagram, AP and BQ are equal and parallel to each other.

Prove that :

(i) $Δ$ AOP $≅ Δ$ BOQ.

(ii) AB and PQ bisect each other.

In $△ A O P a n d △ B O Q$

AP=BQ (given)
$∠ O A P = ∠ O B Q (e a c h 90^{0}$
$∠ A O P = ∠ B O Q$ (vertically opposite angle)

$△ A O P i s ≅ △ B O Q$ (by AAS rule)

By CPCT
OP=OQ
AO=OB
Hence proved