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These shapes have four sides and 360° of interior angle goodness.

# Properties of Parallelograms

In the above diagram, quadrilateral $$ABCD$$ is a parallelogram and $$M$$ is the midpoint of $$\overline{DC}.$$ If the area of $$\triangle BNC$$ is $$42,$$ what is the area of $$\triangle MNC?$$

In the above diagram, $$\angle BAD$$ = $$\angle DCB$$ and $$\angle ADC$$ = $$\angle CBA .$$ If the length of $$\overline{AB}$$ is $$21$$ and the length of $$\overline{AD}$$ is $$16,$$ what is the length of $$\overline{BC}$$?

In the quadrilateral $$ABCD$$ above, $$\overline{AB}$$ is parallel to $$\overline{DC}$$ and $$\overline{AD}$$ is parallel to $$\overline{BC}.$$ If the length of $$\overline{DO}$$= $$41,$$ then what is the length of $$\overline{BO}?$$

In the above diagram, quadrilateral $$ABCD$$ is a parallelogram. If $$\alpha = 69 ^\circ$$ and $$\beta = 55 ^\circ ,$$ what is $$\angle BAC$$?

In the quadrilateral $$ABCD$$ above, let $$\lvert\overline{AB} \rvert$$ denote the length of $$\overline{AB}.$$ If $$\overline{AB}$$ is parallel to $$\overline{DC},$$ $$\lvert\overline{AB}\rvert=\lvert\overline{DC}\rvert = 23,$$ and $$\lvert\overline{AD}\rvert=15,$$ what is $$\lvert\overline{BC}\rvert?$$

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