what is reason for line 5---**Question Stem:**
Complete the proof that m∠RWV + m∠STY = 180°.
**Geometric Diagram Description:**
* Type: Geometric diagram showing lines and angles.
* Elements:
* Three lines: Two parallel lines intersected by a transversal line.
* Parallel lines: One line passing through points S, V, W, R. Another line passing through points Y, P, T, X, U, G. Red arrow markings indicate these lines are parallel.
* Transversal line: Passes through points E, P, W, T, L.
* Points labeled: E, Y, P, S, V, W, T, R, L, X, U, G.
* Angles indicated: ∠RWV, ∠PFR (appears to be ∠PWT from the diagram), ∠STY.
* Relative Position: Line SVR is parallel to line YPUG. Transversal line EPTL intersects both parallel lines. Point W is on SVR, point T is on YPUG, point P is on YPUG and EPTL, point W is on SVR and EPTL, point R is on SVR, point S is on SVR, point V is on SVR, point Y is on YPUG, point X is on YPUG, point U is on YPUG, point G is on YPUG, point E is on EPTL, point L is on EPTL. The angle ∠RWV is formed by line SVR and EPTL. The angle ∠STY is formed by line YPUG and EPTL.
**Proof Table:**
| Statement | Reason |
| :------------------------------ | :---------------------------- |
| 1\. $\overleftrightarrow{VR} \parallel \overleftrightarrow{SU}$ | Given |
| 2\. $\overleftrightarrow{SU} \parallel \overleftrightarrow{YG}$ | Given |
| 3\. ∠RWV ≅ ∠PFR | Corresponding Angles Theorem |
| 4\. m∠PFR + m∠STY = 180° | Same-Side Interior Angles Theorem |
| 5\. m∠RWV + m∠STY = 180° | |
**Missing Information:**
The Reason for Statement 5 is missing. It is the blank cell in the table.
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We have a geometry proof problem involving parallel lines and a transversal. Two parallel lines are cut by a transversal line, creating corresponding angles and interior angles. We need to find the reason for statement 5 in the proof table, which states that the measure of angle RWV plus the measure of angle STY equals 180 degrees.
Let's examine the proof table step by step. Statement 3 tells us that angle RWV is congruent to angle PFR because they are corresponding angles. Statement 4 shows that the measure of angle PFR plus the measure of angle STY equals 180 degrees because they are same-side interior angles. Now we need to determine why statement 5 is true.
The key to understanding statement 5 lies in the substitution property of equality. From statement 3, we know that angle RWV is congruent to angle PFR, which means their measures are equal. Statement 4 gives us an equation with the measure of angle PFR. We can substitute the equal measure of angle RWV in place of the measure of angle PFR, giving us statement 5. This substitution is justified by the substitution property of equality.
Now we can complete the proof table. The reason for statement 5 is the Substitution Property of Equality. This property allows us to replace one quantity with an equal quantity in an equation. Since we established that the measure of angle RWV equals the measure of angle PFR, we can substitute one for the other in the equation. Therefore, the complete answer is: Substitution Property of Equality.
To summarize what we learned: The reason for statement 5 is the Substitution Property of Equality. This property allows us to replace one quantity with an equal quantity in an equation. Since congruent angles have equal measures, we could substitute the measure of angle RWV for the measure of angle PFR. This substitution property is a fundamental tool used throughout geometric proofs.