Question

Write a proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Answer 1

BD^2 = BC^2 + DC^2 (pythagorean theorem, where DC is the diagonal)

Answer 2

AC^2 = DC^2 + AD^2 (also the pythagorean theorem)

Answer 3

BD^2 = BC^2 + DC^2
AC^2 = DC^2 + AD^2

we concluded earlier that BC and AD are congruent (because they're opposite sides of a rectangle)

which means BD^2 and AC^2 are both equal to BC^2 + DC^2

since the side lengths of a rectangle are always positive, we can take the square root of both sides and conclude that

BD = AC = sqrt(BC^2 + DC^2)

^ proving the diagonals are equal

done

Answer 4

*** also I need to mention that angle C and angle A are 90 degree angles (since this is a rectangle) making both triangles right triangles, which is why we can use the pythagorean theorem in the first place

Answer 5

so much lol ok