Question

Solve please pic is given​

Answer 1

Answer:

hey here is your answer in above pics

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Answer 2

Given

• $\textsf{ABCD is a parallelogram }$
• AB = BP
• PQ || BC
• AB=8cm, AD=5cm,AC=10cm

To Solve

1. $\textsf{Prove that point C is mid point of AQ.}$
2. $\textsf{Find the perimeter of quadrilateral BCQP.}$

Solution

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$\\\\\textsf{(1)~~Prove that point C is mid point of AQ.}$

Given : ∆APQ in which B is the Mid-Point of AP and BC || PQ

To Prove : C is the Mid-Point of AQ.

Proof : We have to prove that C is the Mid-Point of AQ if the possible. Let C be not the Mid-Point of AQ. let C' be the Mid-Point of AC . Join BC'

Now , In ∆APQ , B is the Mid-Point of AP and and E' is the Mid-Point of AQ.

Therefore, by Mid-point Theorem, we have

$\sf~~~~~~~~~~~~~~BC' || PQ \: \: \: \: \: \: \: \: \: ~~~~~----(1)$

${\sf~also~~~~~~~~~BC || PQ \: \: \: \: \: \: \: \: \: ~~~~~----(1)[Given ] }$

From (1) and (2) we find that two intersecting lines BC' and BC are both parallel to the line PQ.

This is a contradiction to the parallel lines axiom

So our supposition is wrong,

• Hence C is the midpoint of AQ.

Proved

$\text{\pink{Figure in attachment (1) }}$

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$\\\\\\\textsf{(2)~~Find the perimeter of quadrilateral BCQP.}$

Given

• ABCD is a parallelogram
• AB=8cm, AD=5cm,AC=10cm

To Find

• Perimeter of Quadrilateral BCQP.

Solution

we know that

• In parallelogram opposite sides are Equal.

therefore, AD = BC = 5cm

Also

we know that

• C is the Mid-Point of AQ.

AQ = CQ = 10cm

PQ = 2BC

PQ = 2 × 5cm

PQ = 10cm

Now it is given that, AB = AP

therefore , AP = 8cm

From the above conclusion, we get

CQ = 10cm, BC = 5cm,AP=8cm ,PQ=10cm

Perimeter of BCQP = CQ + BC + AP + PQ

$\textsf{Perimeter of BCQP=10cm+5cm+8cm+10cm}$

Perimeter of BCQP = 33cm.

$\text{\red{Figure in attachment (2) }}$

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