Dani M.

asked • 05/23/19

Need math help, please! Proof

Given: Quadrilateral<math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="18px"><mi>L</mi><mi>M</mi><mi>N</mi><mi>O</mi></mstyle></math> has diagonal <math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="18px"><menclose notation="top"><mi>M</mi><mi>O</mi></menclose></mstyle></math> which splits the quadrilateral into two congruent isosceles triangles.

Prove: <math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="18px"><mi>L</mi><mi>M</mi><mi>N</mi><mi>O</mi></mstyle></math> is a rhombus.

Parallelogram L M N O with diagonal M O is drawn.

1 Expert Answer

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Paul M. answered • 05/23/19

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I will suggest a counterexample.


Consider two isosceles congruent triangles with bases angles = 72°.

The base of each triangle is 1 and each of the equal sides is 1.618.

Put them together so that the vertex of one is at the base of the other.

The figure so formed is a parallelogram that is NOT a rhombus.


Perhaps you submitted the problem incorrectly?


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