In the given figure, ABCD is a parallelogram. AB is produced to P, such that
AB = BP and PQ is drawn parallel to BC to meet AC produced at Q. Given AB = 8
cm, AD = 5 cm, AC = 10 cm.
(i) Prove that point C is mid point of AQ.
(ii) Find the perimeter of quadrilateral BCQP.
Answers
Given: ABCD is a parallelogram. AB = 8 cm, AC = 10 cm, AD = 5 cm, AB is produced to P, AB = BP.
To Find: (i) Prove that point C is midpoint of AQ.
(ii) Find the perimeter of quadrilateral BCQP.
Step-by-step explanation:
(i) In ΔABC and ΔAPQ
∠B = ∠P (corresponding angle are equal since BC║ PQ)
∠C = ∠Q (corresponding angle are equal since BC║ PQ)
∴ ΔABC ≅ ΔAPQ (By AA congruence)
By CPCT
∴ C is the midpoint of AQ.
(ii) Perimeter of quadrilateral BCQP = BC+CQ+QP+BP
BC = AD = 5cm ( opposite sides of parallelogram are equal)
CQ = AC = 10cm (C is the midpoint of AQ)
AB = BP = 8cm (B is the midpoint of AP)
By CPCT (ΔABC ≅ ΔAPQ)
Perimeter = 8 + 10 + 10 + 5 = 23cm
Perimeter of quadrilateral BCQP = 23cm
Step-by-step explanation:
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