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

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #612 : Geometry

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

Possible Answers:

 obtuse and scalene

 is acute and scalene

 is acute and equilateral

 is acute and isosceles, but not equilateral

 is obtuse and isosceles, but not equilateral

Correct answer:

 is acute and equilateral


The figure referenced is below.


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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