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Example Question #1 : Rhombuses
In Rhombus , . If is constructed, which of the following is true about ?
Possible Answers:
is acute and equilateral
is acute and isosceles, but not equilateral
is right and scalene
is acute and scalene
is right and isosceles, but not equilateral
Correct answer:
is acute and isosceles, but not equilateral
Explanation:
The figure referenced is below.
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.
Leann
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