Question

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Answer 1

Step-by-step explanation:

Given:-

ABCD is a Parallelogram and AP||CQ

To find:-

Prove that ∆AOP =~ ∆COQ and APCQ is a Parallelogram

Solution:-

ABCD is a Parallelogram

and AP || CQ

In ∆ AOP and in ∆ COQ

Angle OCQ = Angle OAP

(Alternative Interior angles)

Since AP || CQ and AC is a transversal

angle COQ = angle AOP

(Vertically opposite angles)

angle APO = angle CQO

(Alternative Interior angles)

Since AP || CQ and QP is a transversal

By AAA Property

∆ AOP is congruent to ∆COQ

AP = CQ----------(1)

AO = OC ---------(2)

QO = OP --------(3)

(Corresponding parts in a congruent triangles )

From (2)&(3)

Mid Points are equal

The diagonals are bisecting to each other.

AQ = PC --------(4)

From (1) & (4)

Two pairs of opposite sides are equal.

APCQ is a Parallelogram.

Hence , Proved

Used formulae:-

In a Parallelogram,

• Two pairs of Opposite sides are equal and paralell.
• Diagonals bisect each other.

Answer 2

Answer:

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