Question

prove that the diagonals of a rectangle are congruent answer​

Answer 1

Answer:

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

BC ≅ BC by the Reflexive Property of Congruence.

Furthermore, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB since all right angles are congruent.

Answer 2

Answer:

Step-by-step explanation:

As in the fig AC and BD are two diagonals of

rectangle ABCD

Now in the ΔABC and ΔABD

AB is common

AD=BC( opposite sides)

∠A =∠B=90°

So ΔABC ≅ ΔABD

Thus AC=BD ( Opposite sides of equal angles)

THus both the diagonals of rectangle ABCD are congruent