How to find the length of the diagonal of a rhombus - PSAT Math

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Question

In Rhombus , . If is constructed, which of the following is true about ?

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Answer

The figure referenced is below.

Rhombus

Consecutive angles of a rhombus are supplementary - as they are with all parallelograms - so

A diagonal of a rhombus bisects its angles, so

A similar argument proves that .

Since all three angles of measure , the triangle is acute. It is also equiangular, and, subsequently, equilateral.

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