Given: modifying above upper S upper D with bar perpendicular to modifying above upper H upper T with bar; modifying above upper S upper H with bar congruent to modifying above upper S upper T with bar

Question

Prove:triangleSHD = triangleSTD

Triangle HST is split into two triangles by vertical line SD.A 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.

The image of a two column proof is shown. The left column is titled Statement, and the right column is titled Reason.

Answer 1

Statement Reason
1. Triangle HST is Given
split into two
triangles by line SD
2. HS = ST Given
3. SDSH is a definition of midpoint
parallelogram
4. SAS triangle SAS postulate
congruence (SS)
SDS ~ TDS
5. Triangle SHD ~ CPCTC
triangle STD
6. Angle SHD = definition of congruent
angle STD
7. Triangle SHD = SAS (SSA) congruence
triangle STD theorem