如图,在平行四边形ABCD中,点E是BC的中点,且EA=ED.(1)求证：四边形ABCD是矩形;(2)若BC=6cm,AE=5cm,求S平行四边形ABCD.

Question

如图,在平行四边形ABCD中,点E是BC的中点,且EA=ED.
(1)求证：四边形ABCD是矩形;
(2)若BC=6cm,AE=5cm,求S平行四边形ABCD.

Answer 1

(1)
证明：
在 △AEB 和 △DEC 中：
∵ EA = ED ,EB = EC ,AB = DC
∴ △AEB ≌ △DEC
∴ ∠B = ∠C
∵ AB ∥ DC
∴ ∠B + ∠C = 180°
∴ ∠B = ∠C = 90° ,即平行四边形 ABCD 是矩形.
(2)
EB = BC/2 = 3 (cm)
AE = 5 (cm)
AB² + EB² = AE²
AB = 4 (cm)
S = AB · BC = 24 (cm²)