Q19WE. Write proofs in two-column form.... [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: Q19WE. (page 126)

Write proofs in two-column form.
Given: $E$ is the midpoint of $\overset{炉}{T P}$ ; $E$ is the midpoint of $\overset{炉}{M R}$ .
Prove: $鈻� T E M 鈮� 鈻� P E R$

Short Answer

Expert verified

The two-column proof is:

Statements	Reasons
is the midpoint of $\overset{炉}{T P}$	Given
$\overset{炉}{T E} 鈮� \overset{炉}{P E}$	Definition of midpoint
is the midpoint of $\overset{炉}{M R}$	Given
$\overset{炉}{M E} 鈮� \overset{炉}{R E}$	Definition of midpoint
$鈭� T E M 鈮� 鈭� P E R$	Vertically opposite angles are congruent
$鈻� T E M 鈮� 鈻� P E R$	SAS postulate

Step by step solution

Step 1. Observe the figure.

The figure is:

Step 2. Description of step.

Given that $E$ is the midpoint of $\overset{炉}{T P}$ and $E$ is the midpoint of $\overset{炉}{M R}$ .

Therefore, by using the definition of midpoint, it can be said that $T E = P E$ and $M E = R E$ .

Therefore, $T E 鈮� P E$ and $M E 鈮� R E$ .

From the given diagram it can be noticed that the angles $鈭� T E M$ and $鈭� P E R$ are vertically opposite angles.

Therefore, $鈭� T E M = 鈭� P E R$ .

That implies, $鈭� T E M 鈮� 鈭� P E R$ .

Therefore, it can be seen that $T E = P E$ , $鈭� T E M = 鈭� P E R$ and $M E = R E$ .

Therefore, the triangles $鈻� T E M$ and $鈻� P E R$ are congruent triangles by using the SAS postulate.

Step 3. Write the proof in two-column form.

The proof in two-column form is:

Statements	Reasons
is the midpoint of $\overset{炉}{T P}$	Given
$\overset{炉}{T E} 鈮� \overset{炉}{P E}$	Definition of midpoint
is the midpoint of $\overset{炉}{M R}$	Given
$\overset{炉}{M E} 鈮� \overset{炉}{R E}$	Definition of midpoint
$鈭� T E M 鈮� 鈭� P E R$	Vertically opposite angles are congruent
$鈻� T E M 鈮� 鈻� P E R$	SAS postulate

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91影视

Write proofs in two-column form.
Given: $E$ is the midpoint of $\overset{炉}{T P}$ ; $E$ is the midpoint of $\overset{炉}{M R}$ .
Prove: $鈻� T E M 鈮� 鈻� P E R$

Short Answer

Step by step solution

Step 1. Observe the figure.

Step 2. Description of step.

Step 3. Write the proof in two-column form.

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91影视

Write proofs in two-column form.Given: Eis the midpoint of TP炉; Eis the midpoint of MR炉.Prove: 鈻�TEM鈮�鈻�PER

Short Answer

Step by step solution

Step 1. Observe the figure.

Step 2. Description of step.

Step 3. Write the proof in two-column form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Applied Mathematics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $E$ is the midpoint of $\overset{炉}{T P}$ ; $E$ is the midpoint of $\overset{炉}{M R}$ .
Prove: $鈻� T E M 鈮� 鈻� P E R$