Question

In ∆ABC, angle B=90°, D is the middle point of AC. Prove that BD=1/2 angle AC

Answer 1

This can be proved from studying the congruency of the ∆s one generated by elongating BD further out side in line to that A`D=BD .And joining A`C we get ∆A`CD.Which will be congruent with ABD∆ by theorem of SAS.Which implicates BD=A`D.Again proving the congruency of ∆ABC & A`CB by the theorem of the hypotenuse AC=A`B.A`C=2BD => AC=2BD=>BD=1/2(AC).




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