fill in the blank 5 points
6. given: s is the midpoint of both qp and rt, rs = ps and qs = rt
prove: 2(qs) = qp
statements
1) s is the midpoint of both qp an rt, rs = ps & qs = rt
2) qs ≅ sp and rs ≅ st
3) qs + sp = qp
4) qs + qs = qp
5) 2(qs) = qp
reasons
1) choose your answer...
2) choose your answer...
3) choose your answer...
4) choose your answer...
5) choose your answer...

Question

Accepted Answer

# Explanation:
## Step 1: Reason for Statement 1
The first statement is given in the problem, so the reason is "Given".
## Step 2: Reason for Statement 2
If $ S $ is the midpoint of $ QP $, then by the definition of a midpoint, the segment is divided into two congruent parts. So $ QS \cong SP $ (and similarly $ RS \cong ST $ since $ S $ is the midpoint of $ RT $). The reason is "Definition of Midpoint".
## Step 3: Reason for Statement 3
The statement $ QS + SP = QP $ follows from the Segment Addition Postulate, which states that if a point $ S $ is between $ Q $ and $ P $, then $ QS + SP = QP $. So the reason is "Segment Addition Postulate".
## Step 4: Reason for Statement 4
We know from Statement 2 that $ QS \cong SP $, which means $ QS = SP $ (by the definition of congruent segments). So we can substitute $ SP $ with $ QS $ in the equation from Statement 3. The reason is "Substitution Property (since $ QS = SP $)".
## Step 5: Reason for Statement 5
The equation $ QS + QS = QP $ can be rewritten as $ 2(QS)=QP $ by the definition of multiplication (or the distributive property, where $ a + a = 2a $). The reason is "Definition of Multiplication (or Combining Like Terms)".

# Answer:
1) Given
2) Definition of Midpoint
3) Segment Addition Postulate
4) Substitution Property (since $ QS = SP $)
5) Definition of Multiplication (or Combining Like Terms)

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QUESTION IMAGE

Question

Explanation:

Step 1: Reason for Statement 1

Step 2: Reason for Statement 2

Step 3: Reason for Statement 3

Step 4: Reason for Statement 4

Step 5: Reason for Statement 5

Answer: