91Ó°ÊÓ

If segment \(\underline{A B}\) is parallel to segment \(\underline{C D}\) and \(B C=D C\), prove that \(\underline{\mathrm{BD}}\) bisects \(\angle \mathrm{CBA}\).

Given: \(\underline{A B} \| D C\) and \(\underline{A B} \cong \underline{C D}\). Prove: \(\angle \mathrm{A} \cong \angle \mathrm{C}\).

Given: \(\underline{A C}\) and \(\underline{E B}\) bisect each other at \(D\). Prove: \(\underline{\mathrm{AE}} \| \underline{\mathrm{BC}}\).

Prove that if both pairs of opposite sides of a quadrilateral are congruent, then they are also parallel. Given: Quadrilateral \(\mathrm{ABCD} ; \underline{\mathrm{AB}} \cong \underline{\mathrm{CD}} ; \underline{\mathrm{AD}} \cong \underline{\mathrm{BC}}\) Prove: \(\underline{\mathrm{AD}}\|\underline{\mathrm{BC}} ; \underline{\mathrm{AB}}\| \underline{\mathrm{CD}}\)

In the accompanying figure, \(\underline{A D}=\underline{D C}\) and \(\underline{B D}=\underline{D E}\). Prove that \(\underline{A B} \| \underline{E C}\).

Given: \(\underline{A D}\) and \(\underline{B C}\) intersect at \(E\). \(\underline{A B} \| C D\). \(C E=D E\) Prove: \(A E=B E\).

Given: \(\underline{A D}\|\underline{B E}, \underline{B D}\| \underline{C E}\) and \(B\) is midpoint of \(\underline{A C}\). Prove: \(B E=A D\).

Show that any two medians of a triangle intersect at a point in the interior of the triangle.

Show that the perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices of the triangle.