Q21WE. 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: Q21WE. (page 126)

Write proofs in two-column form.
Given: Plane bisects $\overset{炉}{A B}$ ; $\overset{炉}{P O} 鈯� \overset{炉}{A B}$
Prove: $鈻� P O A 鈮� 鈻� P O B$

Short Answer

Expert verified

The two-column proof is:

Statements	Reasons
bisects $\overset{炉}{A B}$	Given
$\overset{炉}{A O} 鈮� \overset{炉}{B O}$	Definition of midpoint
$\overset{炉}{P O} 鈯� \overset{炉}{A B}$	Given
$m 鈭� P O A = m 鈭� P O B = 90 掳$	Definition of perpendicular lines.
$\overset{炉}{P O} 鈮� \overset{炉}{P O}$	Reflexive property
$鈻� P O A 鈮� 鈻� P O B$	SAS postulate

Step by step solution

Step 1. Observe the figure.

The figure is:

Step 2. Description of step.

Given thatplane $M$ bisects $\overset{炉}{A B}$ and $\overset{炉}{P O} 鈯� \overset{炉}{A B}$ .

Therefore, by using the definition of midpoint, it can be said that $A O = O B$ .

That implies, $A O 鈮� O B$ .

As, $\overset{炉}{P O} 鈯� \overset{炉}{A B}$ , therefore by using the definition of perpendicular lines it can be noticed that $m 鈭� P O A = m 鈭� P O B = 90 掳$ .

In the triangles $鈻� P O A$ and $鈻� P O B$ , it can be noticed that $P O = P O$ by using the reflexive property.

That implies, $P O 鈮� P O$ .

Therefore, it can be seen that $A O = O B$ , $m 鈭� P O A = m 鈭� P O B = 90 掳$ and $P O = P O$ .

Therefore, the triangles $鈻� P O A$ and $鈻� P O B$ are the 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
$M$ bisects $\overset{炉}{A B}$	Given
$\overset{炉}{A O} 鈮� \overset{炉}{B O}$	Definition of midpoint
$\overset{炉}{P O} 鈯� \overset{炉}{A B}$	Given
$m 鈭� P O A = m 鈭� P O B = 90 掳$	Definition of perpendicular lines.
$\overset{炉}{P O} 鈮� \overset{炉}{P O}$	Reflexive property
$鈻� P O A 鈮� 鈻� P O B$	SAS postulate

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91影视

Write proofs in two-column form.
Given: Plane bisects $\overset{炉}{A B}$ ; $\overset{炉}{P O} 鈯� \overset{炉}{A B}$
Prove: $鈻� P O A 鈮� 鈻� P O B$

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: Plane bisects AB炉;PO炉鈯�AB炉Prove:鈻�POA鈮�鈻�POB

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

Discrete Mathematics

Logic and Functions

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: Plane bisects $\overset{炉}{A B}$ ; $\overset{炉}{P O} 鈯� \overset{炉}{A B}$
Prove: $鈻� P O A 鈮� 鈻� P O B$