Which of the following are not necessary when proving that the diagonals of a rectangle are congruent? Check all that apply.
A. All obtuse angles are congruent.
B. All right angles are congruent.
C. Opposite sides are perpendicular.
D. Opposite sides are congruent.
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The Pythagorean theorem will prove it.
By definition, a rectangle has four 90-degree angles, and opposite sides are the same length.
One diagonal line divides the rectangle into two right triangles, with the diagonal as hypotenuse. By the Pythagorean theorem, the length of the hypotenuse is determined by the lengths of the legs.
The other diagonal line divides the rectangle into two different triangles, but these triangles have the same length legs as the other two. So the length of the hypotenuse is exactly the same as before.