Question

Given: ; %0D%0AProve:SHD = STD%0D%0A%0D%0AA triangle is split into two triangles by vertical line SD. The vertex at the bottom left is labeled H. The vertex at the bottom right is labeled T. The vertex at the top in the middle is labeled S. The vertical line down the middle of the triangle starts at point S and ends on line segment HT at a point labeled D. Line segments HS and ST are marked as congruent.

Answer 1

Proof:

Since HS and ST are marked as congruent, we know that triangle SHT is isosceles.

In an isosceles triangle, the altitude from the vertex angle bisects the base. Therefore, HD is perpendicular to ST and bisects it.

This means that SHD and STD are congruent by the base angles theorem.

Therefore, SHD is congruent to STD.