Question

could anyone answer this
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Answer 1

GIVEN: A right triangle ABC. D bisects AC. AD= DC.

TO PROVE: BD = 1/2 AC

CONSTRUCTION: Extend BD up to P, such that BD = DP. Join AP & CP.

In quadrilateral ABCP, diagonals bisect each other. So, ABCP is a parallelogram.

But angle B = 90°

So, parallelogram ABCP should be a rectangle.

Therefore, diagonals AC = BP ( diagonals of a rectangle are equal)

But BP = BD + DP

Since BD = DP by Construction,

BP = BD + BD = 2 BD

Since AC = BP,

 AC = 2 BD

Therefore, BD = AC * 1/2