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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q46. (page 115)

Write a two-column proof.
Given: $\bar{R U} ∥ \bar{S T}$ ; $∠ R ≅ ∠ T$ .
Prove: $\bar{R S} ∥ \bar{U T}$ .

Short Answer

Expert verified

$\bar{R S} ∥ \bar{U T}$

Step by step solution

01

Step 1. Consider the diagram.

Here, $\bar{R U} ∥ \bar{S T}$ and $∠ R ≅ ∠ T$ .

02

Step 2. State the proof.

From the diagram and the information:

$\bar{R U} ∥ \bar{S T}$ and $\bar{U S}$ is transversal.

$∠ 1 ≅ ∠ 2$ .

$∠ R ≅ ∠ T$ and $\bar{U S}$ is common to $Δ U R S$ and $Δ U T S$ .

That implies, $∠ 3 ≅ ∠ 4$ .

That implies, $\bar{R S} ∥ \bar{U T}$

03

Step 3. State the conclusion.

Therefore, $\bar{R S} ∥ \bar{U T}$ . (proved).

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Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior

or corresponding angles

and

Complete each statement with the word always, sometimes, or never.

Lines in two parallel planes are $?$ parallel to each other.

Name the two lines and the transversal that form each pair of angles.

and

Given: $\bar{A S} ∥ \bar{B T}; m ∠ 4 = m ∠ 5$ ; $\vec{S B}$ bisects $∠ A S T$

Find the measure of $∠ 1$

State the postulate or theorem that justifies each statement.

$m ∠ 4 + m ∠ 6 = 180$

See all solutions

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