Question

PQRS is a quadrilateral where A,B,C and D are the midpoints of the sides PQ,RS,QR and SP. PR is the diagonal. Show that
i)DC||PR and DC=1/2 PR
ii)AB=CD
iii)ABCD is a Parallelogram

Answer 1

Here is your answer ❤.

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

(i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR= 2/1

AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ= 2/1

AC.By mid-point theorem. But from (i) SR= 2/1

AC therefore PQ=SR

(iii) PQ∥AC & SR∥AC therefore PQ∥SR and PQ=SR. Hence, a quadrilateral with opposite sides equal and paralle is a parallelogram. Therefore PQRS is a parallelogram.

Answer 2

Answer:

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