Q17WE. Supply the missing statements an... [FREE SOLUTION]

91影视

Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q17WE. (page 126)

Supply the missing statements and reasons.
Given: $\overset{炉}{R S} 鈯� \overset{炉}{S T}$ ; $\overset{炉}{T U} 鈯� \overset{炉}{S T}$ ; is the midpoint of $\overset{炉}{S T}$ .
Prove: $鈻� R S V 鈮� 鈻� U T V$

Short Answer

Expert verified

The complete table is:

Statements	Reasons
$\overset{炉}{R S} 鈯� \overset{炉}{S T}, \overset{炉}{T U} 鈯� \overset{炉}{S T}$	Given
$m 鈭� S = 90 掳, m 鈭� T = 90 掳$	$\overset{炉}{R S} 鈯� \overset{炉}{S T}$ , $\overset{炉}{T U} 鈯� \overset{炉}{S T}$
$鈭� S 鈮� 鈭� T$	$m 鈭� S = m 鈭� T = 90 掳$
$V$ is the midpoint of $\overset{炉}{S T}$	Given
$\overset{炉}{S V} 鈮� \overset{炉}{V T}$	$V$ is the midpoint of $\overset{炉}{S T}$
$鈭� R V S 鈮� 鈭� U V T$	Vertically opposite angles
$鈻� R V S 鈮� 鈻� U V T$	ASA congruence rule

Step by step solution

Step 1. Observe the figure.

The figure is:

Step 2. Description of step.

Given that $\overset{炉}{R S} 鈯� \overset{炉}{S T}$ and $\overset{炉}{T U} 鈯� \overset{炉}{S T}$ .

As $\overset{炉}{R S} 鈯� \overset{炉}{S T}$ , therefore $m 鈭� S = 90 掳$ .

As $\overset{炉}{T U} 鈯� \overset{炉}{S T}$ , therefore $m 鈭� T = 90 掳$ .

Given that $V$ is the midpoint of $\overset{炉}{S T}$ .

As, $V$ is the midpoint of $\overset{炉}{S T}$ , therefore $S V = V T$ .

Therefore, $\overset{炉}{S V} 鈮� \overset{炉}{V T}$ .

From the given diagram it can be noticed that the angles $鈭� R V S$ and $鈭� U V T$ are the vertically opposite angles.

Therefore, the angles $鈭� R V S$ and $鈭� U V T$ have the same measures.

Therefore, $鈭� R V S 鈮� 鈭� U V T$ .

Therefore, it can be seen that $m 鈭� S = m 鈭� T = 90 掳$ , $S V = V T$ and $鈭� R V S = 鈭� U V T$ .

Therefore, the triangles $鈻� R S V$ and $鈻� U T V$ are the congruent triangles by using the ASA postulate.

Step 3. Complete the proof table.

The complete proof table is:

Statements	Reasons
$\overset{炉}{R S} 鈯� \overset{炉}{S T}$ , $\overset{炉}{T U} 鈯� \overset{炉}{S T}$	Given
$m 鈭� S = 90 掳$ , $m 鈭� T = 90 掳$	$\overset{炉}{R S} 鈯� \overset{炉}{S T}$ , $\overset{炉}{T U} 鈯� \overset{炉}{S T}$
$鈭� S 鈮� 鈭� T$	$m 鈭� S = m 鈭� T = 90 掳$
$V$ is the midpoint of $\overset{炉}{S T}$	Given
$\overset{炉}{S V} 鈮� \overset{炉}{V T}$	$V$ is the midpoint of $\overset{炉}{S T}$
$鈭� R V S 鈮� 鈭� U V T$	Vertically opposite angles
$鈻� R V S 鈮� 鈻� U V T$	ASA congruence rule

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91影视

Supply the missing statements and reasons.
Given: $\overset{炉}{R S} 鈯� \overset{炉}{S T}$ ; $\overset{炉}{T U} 鈯� \overset{炉}{S T}$ ; is the midpoint of $\overset{炉}{S T}$ .
Prove: $鈻� R S V 鈮� 鈻� U T V$

Short Answer

Step by step solution

Step 1. Observe the figure.

Step 2. Description of step.

Step 3. Complete the proof table.

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91影视

Supply the missing statements and reasons.Given: RS炉鈯�ST炉;TU炉鈯�ST炉; is the midpoint of ST炉.Prove: 鈻�RSV鈮�鈻�UTV

Short Answer

Step by step solution

Step 1. Observe the figure.

Step 2. Description of step.

Step 3. Complete the proof table.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Supply the missing statements and reasons.
Given: $\overset{炉}{R S} 鈯� \overset{炉}{S T}$ ; $\overset{炉}{T U} 鈯� \overset{炉}{S T}$ ; is the midpoint of $\overset{炉}{S T}$ .
Prove: $鈻� R S V 鈮� 鈻� U T V$