Question

prove that digonals of a rectangle are equal​

Answer 1

Since rectangles have right angles in each corner and opposite sides of a rectangle are congruent, then in rectangle ABCD it would be true that AB is congruent to CD. Therefore by the Pythagorean Theorem:

AB² + BC² = AC² and CD² + BC² = BD²

But since AB = CD, it follows that AB² = CD² so

AB² + BC² = CD² + BC² which simplifies to

AC² = BD²

If AC² = BD² then AC = BD, proving diagonals are of equal length.

I hope that helps.

Answer 2

Answer:

Answer:

ABCD is a rectangle with AC and BD as its diagonals.

ABCD is a rectangle

A = 90o, AD = BC

ADBC and AB is a transversal

A + B = 180o

B = 90o

In ABD and BAC

AB = BA

A = B

AD = BC

ABD BAC (SAS)

BD = AC (c.p.c.t)

Hence, the diagonals of a rectangle are equal.