Question

IF D is the mid-point of the hypontenuse AC of a right triangle ABC. prove that BD=1 2 AC

Answer 1

Extend BD to the point E such that DE =DB and join it with C. Prove the congruency. Consider triangle ADB and triangle EDC. Angle ADB = angle EDB (Vertically opposite angles) DE =DB AD =DC By SAS the two triangle are congruent.