Q8. Given:聽PR炉 bisects 鈭燬PT聽and... [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: Q8. (page 149)

Given: $\overset{炉}{PR}$ bisects $鈭� SPT$ and $鈭� SRT$ .
Prove: $\overset{炉}{PR}$ bisects $鈭� SQT$ .
a. List the key steps of a proof.
b. Write a proof in paragraph form.

Short Answer

Expert verified

$螖 PSR 鈮� 螖 PTR$	ASA property
$\overset{炉}{SR} 鈮� \overset{炉}{TR}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 SQR 鈮� 螖 TQR$	SAS postulate
$\overset{炉}{PR}$ bisects $鈭� SQT$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Statements	Reason
$\overset{炉}{PR}$ bisects $鈭� SPT$ ; $\overset{炉}{PR}$ bisects $鈭� SRT$	Given
$\overset{炉}{PR} 鈮� \overset{炉}{PR}$	Reflexive property
$螖 PSR 鈮� 螖 PTR$	ASA property
$\overset{炉}{SR} 鈮� \overset{炉}{TR}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$\overset{炉}{QR} 鈮� \overset{炉}{QR}$	Reflexive property
$螖 SQR 鈮� 螖 TQR$	SAS postulate
$\overset{炉}{PR}$ bisects $鈭� SQT$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Part a. Step 1. Description of step.

Consider $螖 P S R$ and $螖 P T R$ , As $\overset{炉}{P R}$ bisects $鈭� S P T$ and $鈭� S R T$ which implies, $鈭� S P R 鈮� 鈭� T P R$ and $鈭� S R P 鈮� 鈭� T R P$ . By reflexive property, $\overset{炉}{P R} 鈮� \overset{炉}{P R}$ which implies that $螖 P S R 鈮� 螖 P T R$ by ASA postulate.

Part a. Step 2. Description of step.

As $螖 P S R 鈮� 螖 P T R$ , by corresponding parts of congruent triangles, $\overset{炉}{S R} 鈮� \overset{炉}{T R}$ .

Part a. Step 3. Description of step.

Consider $螖 S Q R$ and $螖 T Q R$ , by reflexive property $\overset{炉}{Q R} 鈮� \overset{炉}{Q R}$ . Also, $\overset{炉}{S R} 鈮� \overset{炉}{T R}$ and $鈭� S R P 鈮� 鈭� T R P$ then by SAS postulate, width="111" height="20" role="math">螖SQR鈮�螖TQR.

Part a. Step 4. Description of step.

As $螖 S Q R 鈮� 螖 T Q R$ , by corresponding parts of congruent triangles, $鈭� S Q R 鈮� 鈭� T Q R$ which implies that $\overset{炉}{P R}$ bisects $鈭� S Q T$ .

Part a. Step 5. Key steps of a proof.

Make a list of key steps of a proof.

$螖 P S R 鈮� 螖 P T R$	ASA property
$\overset{炉}{S R} 鈮� \overset{炉}{T R}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 S Q R 鈮� 螖 T Q R$	SAS postulate
$\overset{炉}{P R}$ bisects $鈭� S Q T$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Part b. Step 1. Description of step.

Part b. Step 2. Description of step.

As $螖 P S R 鈮� 螖 P T R$ , by corresponding parts of congruent triangles, $\overset{炉}{S R} 鈮� \overset{炉}{T R}$ .

Part b. Step 3. Description of step.

Part b. Step 4. Description of step.

As $螖 S Q R 鈮� 螖 T Q R$ , by corresponding parts of congruent triangles, $鈭� S Q R 鈮� 鈭� T Q R$ which implies that $\overset{炉}{P R}$ bisects $鈭� S Q T$ .

Part b. Step 5. Two-column proof.

Write a two-column proof of the above explanation.

Statements	Reason
$\overset{炉}{P R}$ bisects $鈭� S P T$ ; $\overset{炉}{P R}$ bisects $鈭� S R T$	Given
$\overset{炉}{P R} 鈮� \overset{炉}{P R}$	Reflexive property
$螖 P S R 鈮� 螖 P T R$	ASA property
$\overset{炉}{S R} 鈮� \overset{炉}{T R}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$\overset{炉}{Q R} 鈮� \overset{炉}{Q R}$	Reflexive property
$螖 S Q R 鈮� 螖 T Q R$	SAS postulate
$\overset{炉}{P R}$ bisects $鈭� S Q T$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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91影视

Given: $\overset{炉}{PR}$ bisects $鈭� SPT$ and $鈭� SRT$ .
Prove: $\overset{炉}{PR}$ bisects $鈭� SQT$ .
a. List the key steps of a proof.
b. Write a proof in paragraph form.

Short Answer

Step by step solution

Part a. Step 1. Description of step.

Part a. Step 2. Description of step.

Part a. Step 3. Description of step.

Part a. Step 4. Description of step.

Part a. Step 5. Key steps of a proof.

Part b. Step 1. Description of step.

Part b. Step 2. Description of step.

Part b. Step 3. Description of step.

Part b. Step 4. Description of step.

Part b. Step 5. Two-column proof.

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91影视

Given:PR炉 bisects 鈭�SPTand 鈭�SRT.Prove:PR炉 bisects 鈭�SQT.a. List the key steps of a proof.b. Write a proof in paragraph form.

Short Answer

Step by step solution

Part a. Step 1. Description of step.

Part a. Step 2. Description of step.

Part a. Step 3. Description of step.

Part a. Step 4. Description of step.

Part a. Step 5. Key steps of a proof.

Part b. Step 1. Description of step.

Part b. Step 2. Description of step.

Part b. Step 3. Description of step.

Part b. Step 4. Description of step.

Part b. Step 5. Two-column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{PR}$ bisects $鈭� SPT$ and $鈭� SRT$ .
Prove: $\overset{炉}{PR}$ bisects $鈭� SQT$ .
a. List the key steps of a proof.
b. Write a proof in paragraph form.