Your teacher will grade your responses to questions 6–9 to ensure that you receive proper credit for your answers.
Complete the proof by providing the missing statement and reasons.
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
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.
Statement Reason
1. Triangle HSD = Triangle TSD Given (Vertical angles are congruent)
2. Triangle HSD ≅ Triangle TSD Definition of congruence
3. Triangle HSD ≅ Triangle STD Reflexive property of congruence (HS ≅ ST)
4. Triangle SHD ≅ Triangle STD CPCTC (Corresponding parts of congruent triangles are congruent)
Statement Reason
1. Triangle SHT is a right triangle Given
2. Triangle SHD is a right triangle Definition of triangle SHD
3. Angle H is congruent to angle T Given
4. Therefore, triangle SHD is congruent to triangle STD Angle-Angle similarity
5. Triangle SHD = triangle STD Definition of congruent triangles
Statement Reason
1. Triangle HST is split into two triangles by vertical line SD. Given
2. Line SD is perpendicular to line HT. Given
3. Line SH is congruent to line ST. Given
4. Triangle SHD is a triangle. Definition of a triangle
5. Triangle STD is a triangle. Definition of a triangle
6. Angle HSD is congruent to angle STD. Vertical angles are congruent
7. Angle HDS is congruent to angle TDS. Vertical angles are congruent
8. Line HD is congruent to line TD. Common side of the congruent triangles
9. Triangle SHD is congruent to triangle STD. Side-Angle-Side (SAS) congruence theorem.