SOLUTION: Assume that abcd is a rhombus. Prove that ac is prependicular to bd (let e be the point of intersection$

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Question 602872: Assume that abcd is a rhombus. Prove that ac is prependicular to bd (let e be the point of intersection$
Answer by solver91311(24713) About Me  (Show Source):
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Draw the diagonals forming 4 triangles. Since it is a rhombus, it is also a parallelogram. The diagonals of a parallelogram bisect each other.

AB congruent AD, defn of rhombus

AE congruent AE, reflexive equality

BE congruent DE, diagonals of parallelogram bisect each other

Triangle ABE congruent triangle ADE by SSS

Angle BED is a straight angle, hence measures 180 degrees.

Angle AEB congruent Angle AED by CPCT

measure of BED equals measure AEB + measure AED

measure of BED equals 2 times measure AEB

measure AEB is 90

QED.

John

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