Question

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

A. Scalene acute
B. Isosceles
C. Equilateral
D. Scalene obtuse

Answer 1

Using the median and altitude BD for △ABC, along with the SAS congruence postulate, it can be concluded that the triangle is isosceles.

Step-by-step explanation:

The question involves determining what type of triangle △ABC is, given that BD is both the median and altitude of the triangle. Since BD is a median, it divides the base AC into two equal parts, and since it is also an altitude (a line segment perpendicular to a side of the triangle from the opposite vertex), △ABC is symmetric across BD. Therefore, the two triangles formed by the median, △ABD and △CBD, are congruent by the Side-Angle-Side (SAS) postulate because they have a shared side (BD), congruent angles (right angles where BD meets AC), and congruent sides (since BD bisects AC, AD equals CD).

With this symmetry and the congruent triangles, △ABC is an isosceles triangle, having at least two equal sides (AB equals BC in this case).