PSAT Math : How to find an angle in a rhombus

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : Quadrilaterals

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

Possible Answers:

 is right and scalene

 is acute and equilateral

 is right and isosceles, but not equilateral

 is acute and isosceles, but not equilateral

 is acute and scalene

Correct answer:

 is acute and isosceles, but not equilateral

Explanation:

The figure referenced is below.

Rhombus

The sides of a rhombus are congruent by definition, so , making  isosceles. It is not equilateral, since , and an equilateral triangle must have three  angles.

Also, consecutive angles of a rhombus are supplementary - as they are with all parallelograms - so

A diagonal of a rhombus bisects its angles, so 

Similarly, 

This makes  acute.

The correct response is that  is acute and isosceles, but not equilateral.

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