In the figure ACDF is a parallelogram and AD and BE bisect each other. Prove that BC ? FE.


AC ? FD since they are opposite sides in a parallelogram. AG ? GD and BG ? GE because AD and BE bisects each other. ?AGB AND ?EGD are congruent because they are vertical angles. So ?AGB ? ?DGE by SAS. AB ? ED by C.P. Finally, since AB + BC = AC and FE + Ed = FD, BC = FE.


(Outline) Since ?RVT is isosceles with ?V the vertex angle, RV ?VT. Then, in ?RVT,?R ? T since they are opposite congruent sides. VS is the meridian to RT ? RS? ST. Then ?RVS ?TVS by S.A.S. By C.P., ?RVS ? ?TVS. Thus VS bisects ?RVT.

Mathematics

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