Given: a b c d is a rectangle. prove: the diagonals of a b c d are congruent. the coordinates of rectangle abcd are a(0, 0) , b(a, 0) , and d(0, b) . the length of ac¯¯¯¯¯ is equal to the length of bd¯¯¯¯¯ is equal to the diagonals of the rectangle have the same length. therefore, ac¯¯¯¯¯ is congruent to bd¯¯¯¯¯.

The coordinates of C(a,b).

The length of AC diagonal is equal to

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

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

=

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

AC=

AC=

The length of AC diagonal is equal to .

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

BD=

BD=

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.

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step-by-step explanation:

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