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Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD.
transforming the original condition by variable approach method, we have 2 variables for the rhombus (side length and one diagonal side length). Since we need to match the number of variables and equations, we need 2 more equations. Since there is 1 equation each in 1) and 2), C is likely the answer and it turns out that C actually is the answer .
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