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Quadrilaterals

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

Quadrilateral Classification

         

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, 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 \(ABEF ?\)

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.

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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