Question

diagonal of a quadlateral are equal is such a quadlateral always a rectangle if your answer is no draw a figure to justify your answer please tell quickly​

Answer 1

Answer:

No, if the diagonals of the quadrilateral are perpendicular to each other then such quadrilateral is not always a rhombus.

as you know conditions of rhombus

1. it should be parallelogram.

2. all sides should be equal.

3. diagonals are perpendicular to each other.

but here given only " diagonals of the quadrilateral are perpendicular to each other."

hence, we can't say given quadrilateral is always rhombus.

I hope it helped uu... Please mark me brainliest ☺️❤️..

Answer 2

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if the diagonal of parallelogram are equal...

let ABCD be a parallelogram in which AC = BD

in triangle DCB and ACB ,

DC = AB ...(opposite sides of parallelogram)

CB = CB ...(common)

DB = AC ...(given)

hence by SSS congruence rule triangle DCB is congruent to triangle is ACB

by cpct , angle DCB = angle ACB

since ABCD is a parallelogram.. AB parallel to DC and CB in a transversal

angle DCB + angle ACB = 180° (because some of co interior angles is 180)

angle DCB = angle ACB = 90°

hence , ABCD is a parallelogram one of whose angle is 90°

therefore ABCD is a rectangle

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