pls answer the 15th one
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Answer:
Step-by-step explanation:
given: a parallelogram pqrs
TO PROVE : PR²+QS² = PQ²+QR²+RS²+SP²
proof:
AD is a median ofΔABC
AB²+AC² = 2(AD²+BD²)
AB²+AC² = 2AD²+1/2BC²
THE DIAGONAL OF PARALLELOGRAM BISECT EACH OTHER
O IS THE MIDPOINT OF PR AND AS WELL AS QS
INΔPQR AND ΔRSP
PQ²+QR² = 2OQ²+1/2PR² -----------------(1)
AND RS²+SP² =2OS²+1/2PR²------------(2)
ADD (1) AND (2)
PQ² + QR² + RS² + SP² = 2(1/2 X QS²) + 2(1/2 X QS²) + PR²
PQ²+QR²+RS²+SP² = PR² + QS² HENCE PROVED
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