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Complete the following proof.

Prove: The diagonals of a square are perpendicular.

For AC:
the slope is:
AC=(y2-y1)/(x2-x1)
AC=(a-0)/(a-0)
AC=(a)/(a)
AC=1

For BD:
the slope is:
BD=(0-a)/(a-0)
BD=(-a)/(a)
BD=-1

AC is perpendicular to BD

Answer:
AC is perpendicular to BD

Answer Link

akposevictor akposevictor · Answer 2 · 2022-06-01T17:17:21+02:00

The slope of AC is 1

The slope of BD is -1.

Therefore, the diagonals of the square are perpendicular.

What are the Diagonals of a Square?

Diagonals of a square bisect each other perpendicularly and therefore have slopes that are negative reciprocals. This means that, if the slopes both diagonals of a square are multiplied together, the result must be -1.

Slope of AC = change in y / change in x = (a-0) / (a-0) = a/a = 1

Slope of BD = change in y / change in x = (0-a) / (a-0) = -a/a = -1

Slope of BD × slope of AC = -1 × 1 = -1

Therefore, the diagonals of square ABCD are perpendicular.

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