QS TV. Complete the proof that ZVUW ≈ ZPRQ. P 1 2 3 4 R S V U T Statement 3 QSI TV ZVUW ZSRU ZSRU ZPRQ ZVUW ZPRQ Reason
QS TV. Complete the proof that ZVUW ≈ ZPRQ. P 1 2 3 4 R S V U T Statement 3 QSI TV ZVUW ZSRU ZSRU ZPRQ ZVUW ZPRQ Reason
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Parallel Lines and Angle Congruency Proof**
In the diagram, lines \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) are parallel, as indicated by the parallel line symbols. The objective is to complete the proof that \(\angle VUW \cong \angle PRQ\).
The diagram is composed of two parallel lines (\(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\)), intersected by two transversals (\(\overleftrightarrow{PU}\) and \(\overleftrightarrow{RW}\)). The points are labeled as follows: \(P\), \(S\), \(V\) on the first transversal, \(Q\), \(T\), \(W\) on the second transversal, and \(R\) and \(U\) are the intersection points with the parallel lines.
Below the diagram, a table outlines the proof structure, with columns for "Statement" and "Reason". The goal is to fill in this table with logical steps and justifications to prove the desired angle congruency.
**Proof Table:**
1. **Statement:** \( \overleftrightarrow{QS} \parallel \overleftrightarrow{TV} \)
**Reason:** [Select Reason]
2. **Statement:** \(\angle VUW \cong \angle \text{SRU}\)
**Reason:** [Select Reason]
3. **Statement:** \(\angle \text{SRU} \cong \angle \text{PRQ}\)
**Reason:** [Select Reason]
4. **Statement:** \(\angle VUW \cong \angle \text{PRQ}\)
**Reason:** [Select Reason]
**Explanation of Relationship:**
- \(\angle VUW\) and \(\angle PRQ\) are corresponding angles formed by the intersection of the transversals with the parallel lines.
- The congruency of these angles can be established using properties of parallel lines and transversals, such as corresponding angles or alternate interior angles being congruent.
In the educational context, understanding these geometric relationships helps in developing spatial reasoning and logical thinking as part of learning proofs in geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed6b863d-4462-4a63-ab35-b20a174184a4%2F0786da8e-be36-4cac-8756-44410cd916b3%2Fjn56qm_processed.png&w=3840&q=75)
Transcribed Image Text:**Parallel Lines and Angle Congruency Proof**
In the diagram, lines \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) are parallel, as indicated by the parallel line symbols. The objective is to complete the proof that \(\angle VUW \cong \angle PRQ\).
The diagram is composed of two parallel lines (\(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\)), intersected by two transversals (\(\overleftrightarrow{PU}\) and \(\overleftrightarrow{RW}\)). The points are labeled as follows: \(P\), \(S\), \(V\) on the first transversal, \(Q\), \(T\), \(W\) on the second transversal, and \(R\) and \(U\) are the intersection points with the parallel lines.
Below the diagram, a table outlines the proof structure, with columns for "Statement" and "Reason". The goal is to fill in this table with logical steps and justifications to prove the desired angle congruency.
**Proof Table:**
1. **Statement:** \( \overleftrightarrow{QS} \parallel \overleftrightarrow{TV} \)
**Reason:** [Select Reason]
2. **Statement:** \(\angle VUW \cong \angle \text{SRU}\)
**Reason:** [Select Reason]
3. **Statement:** \(\angle \text{SRU} \cong \angle \text{PRQ}\)
**Reason:** [Select Reason]
4. **Statement:** \(\angle VUW \cong \angle \text{PRQ}\)
**Reason:** [Select Reason]
**Explanation of Relationship:**
- \(\angle VUW\) and \(\angle PRQ\) are corresponding angles formed by the intersection of the transversals with the parallel lines.
- The congruency of these angles can be established using properties of parallel lines and transversals, such as corresponding angles or alternate interior angles being congruent.
In the educational context, understanding these geometric relationships helps in developing spatial reasoning and logical thinking as part of learning proofs in geometry.
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