Properties of Squares


True or False?

Connecting the consecutive midpoints of the four sides of any simple quadrilateral makes a parallelogram.

Square ABCDABCD has side length equal to 1212. EE is the midpoint of ADAD and FF is the midpoint of DCDC. What is the area of quadrilateral BEFCBEFC?

ABCDABCD is a square such that [ABCD]=120 [ABCD] = 120 . E,F,G,HE, F, G, H are the midpoints of AB,BC,CD AB, BC, CD and DADA respectively. What is [EFGH] [EFGH] ?

Details and assumptions

[PQRS][PQRS] denotes the area of figure PQRSPQRS.

Square ABCDABCD has MM as the midpoint of ABAB, NN as the midpoint of BCBC, PP as the midpoint of CDCD and QQ as the midpoint of MPMP. If [AMNPDQ]=50[AMNPDQ] = 50, what is the value of [ABCD][ABCD]?

Details and assumptions

[PQRS][PQRS] refers to the area of figure PQRSPQRS.

How many sides of a square have equal length?


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