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

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.

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\(ABCD\) 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.

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In the above diagram, figure \(ABCD\) is a parallelogram where \(\lvert{\overline{AB}} \rvert =6\) and \(\lvert{\overline{AD}}\rvert=8.\) If the angle bisectors of \(\angle A\) and \(\angle B\) intersect with \(\overline{BC}\) and \(\overline{AD}\) at \(E\) and \(F,\) respectively, which of the following must be true of quadrilateral \(ABEF ?\)

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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.

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Figure \(ABCD\) is s square with side length \(12\) and \[\lvert{\overline{EB}}\rvert =\lvert{\overline{FC}}\rvert=\lvert{\overline{GD}}\rvert=\lvert{\overline{HA}}\rvert=9.\] What type of quadrilateral is \(EFGH\)?

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