Question

Given: A B C D is a rectangle.

Answer 1

Answer:

The coordinates of C(a,b).

The length of AC diagonal is equal to $\sqrt{a^2+b^2}$

The length of BD diagonal is equal to $\sqrt{a^2+b^2}$.

Therefore, AC diagonal is congruent to BD diagonal.

Step-by-step explanation:

Given

ABCD is a rectangle.

AB=CD and BC=AD

$m\angle A= m\angle B= m\angle C=m\angle D=90^{\circ}$

The coordinates of rectangle ABCD are A(0,0),B(a,0),C(a,b) and D(0,b).

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula

=$\sqrt{(x-2-x_1)^2+(y_2-y_1)^2}$

The distance between two points A (0,0) and C(a,b)

AC=$\sqrt{( a-0)^2+(b-0)^2}$

AC= $\sqrt{(a^2+b^2)}$

The length of AC diagonal is equal to $\sqrt{(a^2+b^2)}$.

Distance between the points B(a,0) and D(0,b)

BD=$\sqrt{(0-a)^2+(b-0)^2}$

BD=$\sqrt{(a^2+b^2)}$

The length of BD diagonal is equal to $\sqrt{(a^2+b^2)}$.

The diagonals of the rectangle have the same length.

Therefore, AC diagonal is congruent to BD diagonal.

Hence proved.

Answer 2

C = (b, a)

AC = BD
BD = AC