complete the proof that $ \triangle vwx \cong \triangle uty $.

Question

Accepted Answer

# Explanation:
## Step1: Identify the reason for $\overline{XY}\cong\overline{UV}$
From the figure, the segments $\overline{XY}$ and $\overline{UV}$ are marked with the same number of tick - marks. So the reason is "Given (marked on the diagram)".
## Step2: Identify the reason for $\overline{VW}\cong\overline{TU}$
The segments $\overline{VW}$ and $\overline{TU}$ are marked with the same number of tick - marks. So the reason is "Given (marked on the diagram)".
## Step3: Identify the reason for $\overline{TY}\cong\overline{WX}$
The segments $\overline{TY}$ and $\overline{WX}$ are marked with the same number of tick - marks. So the reason is "Given (marked on the diagram)".
## Step4: Identify the reason for $UY = XY+UX$
By the segment addition postulate (if we have two adjacent segments $XY$ and $UX$ that form a larger segment $UY$). So the reason is "Segment Addition Postulate".
## Step5: Identify the reason for $VX = UV + UX$
By the segment addition postulate (if we have two adjacent segments $UV$ and $UX$ that form a larger segment $VX$). So the reason is "Segment Addition Postulate".
## Step6: Identify the reason for $UY=UV + UX$
Since $XY\cong\overline{UV}$, then $XY = UV$. Substitute $XY$ with $UV$ in the equation $UY=XY + UX$ (by substitution property of equality). So the reason is "Substitution Property ($XY = UV$)".
## Step7: Identify the reason for $VX = UY$
Since $VX=UV + UX$ and $UY = UV+UX$, by transitive property of equality (if $a=b$ and $b = c$, then $a=c$). So the reason is "Transitive Property ($VX=UV + UX$ and $UY = UV + UX$)".
## Step8: Identify the reason for $\triangle VWX\cong\triangle UTY$
We have $\overline{VW}\cong\overline{TU}$, $\overline{WX}\cong\overline{TY}$, and $\overline{VX}\cong\overline{UY}$. By SSS (Side - Side - Side) congruence criterion. So the reason is "SSS Congruence Criterion".

# Answer:
1. Given (marked on the diagram)
2. Given (marked on the diagram)
3. Given (marked on the diagram)
4. Segment Addition Postulate
5. Segment Addition Postulate
6. Substitution Property ($XY = UV$)
7. Transitive Property ($VX=UV + UX$ and $UY = UV + UX$)
8. SSS Congruence Criterion

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the reason for \(\overline{XY}\cong\overline{UV}\)

Step2: Identify the reason for \(\overline{VW}\cong\overline{TU}\)

Step3: Identify the reason for \(\overline{TY}\cong\overline{WX}\)

Step4: Identify the reason for \(UY = XY+UX\)

Step5: Identify the reason for \(VX = UV + UX\)

Step6: Identify the reason for \(UY=UV + UX\)

Step7: Identify the reason for \(VX = UY\)

Step8: Identify the reason for \(\triangle VWX\cong\triangle UTY\)

Answer: