Question
Short Answer
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: SD upside down t HT ; SH wingle = ST
Prove: triangle SHD = triangle STD
Shape: Triangle HST is split into two triangles by vertical line SD.
statement reason
2. Angle SDH and Angle SDT are right angle s 2.?
3. SH ~= ST 3. ?
4. ? 4. Reflexive Property
5. triangle SHD ~= STD 5. ?
2. Angle SDH and Angle SDT are right angles. Given: "SD upside down t HT" (meaning triangle SDH is congruent to triangle SDT)
3. SH ~= ST. Given: "SH wingle = ST" (meaning segment SH is congruent to segment ST)
4. SH ~= SH. Reflexive Property of Congruence (Any segment is congruent to itself)
5. triangle SHD ~= STD. Angle-Side-Angle (ASA) Congruence Theorem (If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the two triangles are congruent)
statement reason
2. Angle SDH and Angle SDT are right angles 2. Definition of perpendicular lines
3. SH ~= ST 3. Given: SH congruent to ST
4. HD ~= TD 4. Definition of congruent segments
5. triangle SHD ~= triangle STD 5. SSS postulate
To complete the proof, we need to provide the missing statements and reasons.
Given: SD upside down t HT ; SH wingle = ST
Prove: triangle SHD = triangle STD
Shape: Triangle HST is split into two triangles by vertical line SD.
Statement Reason
2. Angle SDH and Angle SDT are right angles 2. Given (SD is perpendicular to HT)
3. SH is congruent to ST 3. Given (SH is equal to ST)
4. Angle SDH is congruent to Angle SDT 4. Definition of Right Angles (both angles are right angles)
5. triangle SHD is congruent to triangle STD 5. SAS Congruence Postulate (two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle)
Therefore, we have proven that triangle SHD is congruent to triangle STD.