Question

Complete the coordinate proof of the theorem. Given: A B C D is a rectangle. Prove: The diagonals of A B C D are congruent.

Answer 1

Answer:

all the side but to are eaual you must divide by two then go

Answer 2

Step-by-step explanation:

Given coordinates of the rectangle ABCD:

• A(0, 0), B(a, 0), C(x, y), D(0, b)

Lets first find coordinates of C

We can see that A and B are on same line horizontally, so C and D will be on the parallel line

The distance AB and CD are equal also distance AD and BC are equal, therefore

• AB = a - 0 = a, CD = a
• AD = b - 0 = b, BC = b

So the coordinates of C are:

• x = a, y = b

Now the diagonals:

• AC = √(a-0)² + (b-0)² = √a²+b²
• BD =√(0-a)² + (b -0)² = √a² + b²

Since AC = BD, we can state they are congruent