Question

9. In the following diagram, AP and BQ are
equal and parallel to each other.
P
B
А
Prove that:
(i) A AOP = A BOQ.
(ii) AB and PQ bisect each other.​

Answer 1

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

$\bf\underline{\underline{\orange{ Question:-}}}$

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.

$\bf\underline{\underline{\orange{ Answer:-}}}$

ln ∆ AOP & ∆ BOQ

AP=QB. (Given)

<POA= <BOQ. (vertically opposite angle)

<PAO=<QBO. (Alternate interior angle)

∴ ∆AOP ≅ ∆ BOQ. (by A.A.S. criteria)

since,∆AOP ≅ ∆ BOQ. therefore,they both are equal to each other.which prove AO and OB and PO and OQ are equal.

therefore,AB and PQ bisect each other.

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

$\bf\underline{\underline{\orange{ thanks:-}}}$