Question

If line bd is both the altitude and median of triangle abc then triangle abc is

a. obtuse scaleneb. cannot determinec. acute scalned. isosceles

Answer 1

Answer: isosceles

Explanation:

Answer 2

We have a triangle ΔABC, given that BD is both the altitude and median of triangle ΔABC. It means BD⊥AC and AD=DC.

Now we have two Right triangles ΔBDA and ΔBDC such that:-

1. BD = BD (reflexive property)

2. ∡BDA = ∡BDC = 90° (because BD⊥AC; BD is altitude)

3. DA = DC ( because median BD bisects AC into DA=DC)

4. ΔBDA ≡ ΔBDC (Side-Angle-Side congruency of triangles)

5. BA = BC (CPCTC: corresponding parts of congruent triangles are congruent)

In triangle ABC, if AB = BC then we can say that ΔABC is an isosceles triangle.

Hence, option D i.e. Isosceles triangle is the final answer.