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Properties of Parallelograms


In the diagram to the right, quadrilateral ABCDABCD is a parallelogram and MM is the midpoint of DC.\overline{DC}.

If the area of BNC\triangle BNC is 42,42, what is the area of MNC?\triangle MNC?

In the above diagram, BAD\angle BAD = DCB\angle DCB and ADC\angle ADC = CBA.\angle CBA . If the length of AB\overline{AB} is 2121 and the length of AD\overline{AD} is 16,16, what is the length of BC\overline{BC} ?

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

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

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


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