Question

given that BD is both the median and altitude of triangle ABC, congruence postulate SAS is used to prove that triangle ABC is what type of triangle?

Answer 1

Isosceles (apex)

Explanation:

Answer 2

Isosceles

Explanation:

Consider triangle ABC, BD is the median and the altitude drawn to the side AC. This segment (BD) divide the triangle ABC into two triangles: ABD and CBD.

In these triangles:

• AD=DC (because BD is the median);
• ∠ADB=∠CDB=90° (because BD is the altitude);
• BD is common side.

Thus, by SAS postulate, triangles ABD and CBD are conruent. Congruent triangles have congruent corresponding sides. Hence, AB=CB.

If in triangle ABC, AB=BC, then this triangle is isosceles.