supply the missing reasons to complete the proof. given: q=t and qr=tr prove: pr=sr statements: reasons: 1.q=t & qr=tr 1. given 2. pqr =srt 2. vertical angles are = 3. pqr=srt 3. _______ 4.pr=sr 4._______
Answers
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Answer:
ASA, CPCTC
Step-by-step explanation:
1. Given ∠Q ≡ ∠T and QR ≡ TR (Reason : Given)
2. ∠PRQ ≡ ∠SRT (Reason : Vertical Angles)
3. Δ PRQ = ΔSRT (Reason: ASA)
4. PR ≡ SR (Reason : CPCTC)
Explanation for point 3:
∠Q ≡ ∠T (Same Angle)
QR ≡ TR (Equal side)
∠PRQ ≡ ∠SRT (Same Angle)
This comply to the property of ASA
Explanation for point 4:
Since all the corresponding parts of congruent triangles are congruent (CPCTC)
It proves that that PR ≡ SR
Answer:
Step-by-step explanation:
Explain
Statement | Proof
1. angle Q is congruent| 1. Given
to angle T and line QR |
is congruent to line TR|
2. angle PRG is |2. Vertical angles
congruent to angle SRT | are congruent
3. triangle PQR is |3. ?
congruent to triangle |
SRT |
4. line PR is congruent|4. ?
to line SR
2. Complete the proof by providing the missing statement and reasons
Given: Line SD is perpendicular to HT; line SH is congruent to line ST
Prove: triangle SHD is equal to triangle STD
Statement Reason
1. line SD is |1. Given
perpendicular to line |
HT |
2. angle SHD and line |
SDT are right angles |2.?
3. line SH is congruent|3.?
to line ST |
4. ? |4. reflexive
|property
5. Triangle SHD is |5.?
congruent to triangle |
STD |
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