Question

Prove
and
that diagonals of a rectangle
qual
each angle
angle is 90°​

Answer 1

Step-by-step explanation:

sup7riyaTamys

08.12.2016

Math

Secondary School

+8 pts

Answered

Prove each angle of rectangle is 90

2

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Solution:-

Let us consider a rectangle ABCD.

We know that the diagonals of a rectangle are equal. Therefore, AC = DB

In triangle ABC and triangle DCB,

AB = DC (Opposite sides of a parallelogram)

AC = DB

BC = CB (Common side)

Therefore, triangle ABC is congruent to triangle DCB.

And, angle ABC = angle DCB (CPCT)

And, angle ABC + angle DCB = 180° (Adjacent angles of a parallelogram are supplementary/Co interior angles)

Therefore, angle ABC = angle DCB = 90°

And, angle ABC = angle ADC = 90° and angle DCB = angle BAC = 90° (Opposite angles of a parallelogram are equal.)

Hence, each angle of a rectangle measures 90°

Hence proved.

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Answer 2

Answer:

in rectangular opposite side are equal and each 90 degree, so diagonal also same as

draw a diagonal and using pgt in both triangle so we found both are 90 degree