Geometry
# Quadrilaterals

Figure \(ABCD\) is a parallelogram with \(\lvert{\overline{AB}} \rvert =7\) and \(\lvert{\overline{AD}}\rvert=10.\) If the points \(E,F,G\) and \(H\) are intersections between the angular bisectors of the four internal angles of the the parallelogram, what type of quadrilateral is \( EFGH\)?

**Note:** The above diagram is not drawn to scale.

\(ABCD\) is a parallelogram and point \(M\) is the midpoint of side \(\overline{AD}\) where \[\lvert{\overline{AB}}\rvert=10, \lvert{\overline{AD}}\rvert=12.\] If \(\lvert{\overline{BM}}\rvert=\lvert{\overline{CM}}\rvert,\) what type of quadrilateral is \(ABCD\)?

**Note:** The above diagram is not drawn to scale.

In the above diagram, points \(E\) and \(F\) are the feet of perpendiculars drawn from vertex \(A\) of parallelogram \(ABCD\) to sides \(\overline{BC}\) and \(\overline{CD},\) respectively. If \[\lvert{\overline{AE}}\rvert=\lvert{\overline{AF}}\rvert=13,\] what type of quadrilateral is \(ABCD\)?

**Note:** The above diagram is not drawn to scale.