Question

Prove c is the midpoint of AQ
​

Answer 1

In APQ

B is midpoint of AB

BC is parallel to QP

C is midpoint of AQ

(midpoint theorem)

Answer 2

C is the midpoint of AQ, AC = CQ

Perimeter of quadrilateral BCQP is 33 cm.

Step-by-step explanation:

Given :

ABCD is parallelogram

AB=BP

PQ ║BC

AB = 8 cm, AD = 5 cm, AC = 10 cm

1. To Prove C is the midpoint of AQ
2. To find perimeter of quadrilateral BCQP

To Prove C is the midpoint of AQ, AC = CQ

Lets consider Δ APQ

AB = BP = 8 cm (given)

Hence B is the midpoint of AP

PQ ║BC (given )

According to the midpoint theorem,

AC = CQ = 10 cm ...... (1)

Thus its proved that C is the midpoint of AQ.

To find perimeter of quadrilateral BCQP

Perimeter of the quafrilateral BCQP = BC + CQ + QP + BP

BC = 5  cm ( AD = 5 cm , AD = BC as ABCD is a prallelogram)

CQ = 10 cm (from equation (1))

BP = 8 cm (given)

Let QP be X

In Δ ABC and Δ APQ

$\frac{\text{AB}}{\text{AP}} = \frac{\text{BC}}{PQ}$

(AP = AB+BP = 8 + 8 = 16 cm)

$\frac{8}{16} = \frac{5}{X}$

8X = 5 x 16

$\text{X}= \frac{80}{8} = 10 \text{cm}$

∴ Perimeter = 5 + 10 + 10 +8 = 33 cm

To Learn More....

1. What is the perimeter of a quadrilateral whose four sides measure 19/6 , 11/4 ,53/12 , 5/2

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2. Prove that in a quadrilateral ABCD,perimeter is greater than twice of any side

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