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