ABCD is a parallelogram with AC = BD = 6.5cm , ABCD can be
Parallelogram
Trapeziam
Rectangle
Rhombus
Answers
Answer:
rhombus and parallelogram
Given : ABCD is a parallelogram with AC = BD = 6.5cm
To Find : ABCD can be
Parallelogram
Trapezium
Rectangle
Rhombus
Solution:
ABCD is a parallelogram
=> AB = CD and BC = AD as opposite sides of parallelogram are equal ∠A+∠B = 180° sum of adjacent angles in parallelogram is supplementary
in ΔABD and ΔBAC
AB = BA
BD = AC
AD = BC
=> ΔABD ≅ ΔBAC (SSS)
=> ∠A = ∠B
Hence ∠A+∠B = 180°
=> ∠A = ∠B = 90°
Similarly ∠C = ∠D = 90°
Hence parallelogram must be a RECTANGLE
As its given ABCD is a parallelogram so no doubt that ABCD is a parallelogram
if AB = BC then ABCD can be a square which is also rhombus.
But ABCD can not be Trapezium as trapezium has only pair of opposite side parallel while parallelogram has two pair of opposite side parallel.
ABCD is a parallelogram with AC = BD = 6.5cm , ABCD must be a Rectangle
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