You know that a rhombus is simply a parallelogram with four congruent sides. Furthermore, you only need to know that two consecutive sides are congruent in order to prove the parallelogram is indeed a rhombus. Aside from these characteristics, the rhombus has other interesting properties--particularly the properties of its diagonals. The rhombus diagonals do something special to the angles at each vertex. Play the game below to see if you can figure out what they do.
Click here to begin.
Diagonal AC angle A. |
bisects
supplements
complements
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Correct!
What is the relationship between ∠BAC and ∠CAD?
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Diagonal AC angle C. |
bisects
supplements
complements
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Correct!
Did you notice that ∠BCA \(\small\mathsf{\cong}\) ∠DCA?
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Diagonal BD angle B. |
bisects
supplements
complements
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Correct!
What is the relationship between ∠ABD and ∠DBC?
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Diagonal BD angle D. |
bisects
supplements
complements
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Correct!
Did you notice that ∠ADB \(\small\mathsf{\cong}\) ∠CDB?
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Complete
Question
Based on the activity you just completed, each diagonal of a rhombus performs what operation on the vertices, i.e,. the opposite angles?
Each rhombus diagonal bisects a pair of opposite angles.