Question

URGENT!!! please help me with these two problems, and solve with statement-reasoning. Thank you!!!

Answer 1

Answer:

See below.

Step-by-step explanation:

By definition the median of the triangle bisects the  base of the isosceles triangle.

We need to prove that the 2 triangles formed by the median are congruent.

If the 2 triangles are ABD  and ACD  where BD is the median and < ABC is the angle from which BD is drawn.

BD = BD  ( the common side)

AD = DC ( because BD is the median).

AB =  AC ( because ABC is  an isosceles triangle).

So Triangles ABD and ACD are congruent by SSS.

Therefore  m < ABD = m <  CBD,  so BD is the bisector of < ABC.

To prove BD is also the altitude:

Triangles ABD and CBD are congruent as we have just proven. Therefore the

of measure of the base angle ABD = m < CBD . Also they are adjacent angles ( on the same line) so they add up to 180.

Therefore angles ABD and CBD are both  right angles and BD is the altitude of triangle ABC.