Answer:
The coordinates of C(a,b).
The length of AC diagonal is equal to ![\sqrt{a^2+b^2}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%2Bb%5E2%7D)
The length of BD diagonal is equal to
.
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}](https://tex.z-dn.net/?f=m%5Cangle%20A%3D%20m%5Cangle%20B%3D%20m%5Cangle%20C%3Dm%5Cangle%20D%3D90%5E%7B%5Ccirc%7D)
The coordinates of rectangle ABCD are A(0,0),B(a,0),C(a,b) and D(0,b).
Distance between two points
and
is given by the formula
=![\sqrt{(x-2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
The distance between two points A (0,0) and C(a,b)
AC=![\sqrt{( a-0)^2+(b-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%20a-0%29%5E2%2B%28b-0%29%5E2%7D)
AC= ![\sqrt{(a^2+b^2)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28a%5E2%2Bb%5E2%29%7D)
The length of AC diagonal is equal to
.
Distance between the points B(a,0) and D(0,b)
BD=![\sqrt{(0-a)^2+(b-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%280-a%29%5E2%2B%28b-0%29%5E2%7D)
BD=![\sqrt{(a^2+b^2)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28a%5E2%2Bb%5E2%29%7D)
The length of BD diagonal is equal to
.
The diagonals of the rectangle have the same length.
Therefore, AC diagonal is congruent to BD diagonal.
Hence proved.