Q9. Write proofs in the form specifi... [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: Q9. (page 150)

Write proofs in the form specified by your teacher (two-column form, paragraph) form, or a list of key steps).
Given: $螖 RST 鈮� 螖 XYZ$ ; $\overset{炉}{SK}$ bisects $鈭� RST; \overset{炉}{YL}$ bisect $鈭� XYZ$
Prove: $\overset{炉}{SK} 鈮� \overset{炉}{YL}$

Short Answer

Expert verified

Statements	Reason
$螖 RST 鈮� 螖 XYZ$	Given
$鈭� RST 鈮� 鈭� XYZ$ , $\overset{炉}{ST} 鈮� \overset{炉}{YZ}$ and $鈭� T 鈮� 鈭� Z$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$\overset{炉}{SK}$ bisects $鈭� RST$ and $\overset{炉}{YL}$ bisects $鈭� XYZ$	Given
$鈭� TSK 鈮� 鈭� ZYL$	Angle bisector
$螖 SKT 鈮� 螖 YLZ$	ASA postulate
$\overset{炉}{SK} 鈮� \overset{炉}{YL}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Description of step.

As it is given that $螖 R S T 鈮� 螖 X Y Z$ then by corresponding parts of congruent triangles, $鈭� R S T 鈮� 鈭� X Y Z$ , $\overset{炉}{S T} 鈮� \overset{炉}{Y Z}$ and $鈭� T 鈮� 鈭� Z$ .

Step 2. Description of step.

As $\overset{炉}{S K}$ bisects $鈭� R S T$ and $\overset{炉}{Y L}$ bisects $鈭� X Y Z$ then, $鈭� R S T = 2 鈭� T S K$ and $鈭� X Y Z = 2 鈭� Z Y L$ . Since, $鈭� R S T 鈮� 鈭� X Y Z$ implies $鈭� T S K 鈮� 鈭� Z Y L$ .

Step 3. Description of step.

Consider $螖 S K T$ and $螖 Y L Z$ , in which $\overset{炉}{S T} 鈮� \overset{炉}{Y Z}$ , $鈭� T 鈮� 鈭� Z$ and $鈭� T S K 鈮� 鈭� Z Y L$ then by ASA postulate, $螖 S K T 鈮� 螖 Y L Z$ .

Step 4. Description of step.

As $螖 S K T 鈮� 螖 Y L Z$ , by corresponding parts of congruent triangles, $\overset{炉}{S K} 鈮� \overset{炉}{Y L}$ .

Step 5. Two-column proof.

Write a two-column proof of the above explanation.

Statements	Reason
$螖 R S T 鈮� 螖 X Y Z$	Given
$鈭� R S T 鈮� 鈭� X Y Z$ , $\overset{炉}{S T} 鈮� \overset{炉}{Y Z}$ and $鈭� T 鈮� 鈭� Z$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$\overset{炉}{S K}$ bisects $鈭� R S T$ and $\overset{炉}{Y L}$ bisects $鈭� X Y Z$	Given
$鈭� T S K 鈮� 鈭� Z Y L$	Angle bisector
$螖 S K T 鈮� 螖 Y L Z$	ASA postulate
$\overset{炉}{S K} 鈮� \overset{炉}{Y L}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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91影视

Write proofs in the form specified by your teacher (two-column form, paragraph) form, or a list of key steps).
Given: $螖 RST 鈮� 螖 XYZ$ ; $\overset{炉}{SK}$ bisects $鈭� RST; \overset{炉}{YL}$ bisect $鈭� XYZ$
Prove: $\overset{炉}{SK} 鈮� \overset{炉}{YL}$

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Two-column proof.

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91影视

Write proofs in the form specified by your teacher (two-column form, paragraph) form, or a list of key steps).Given: 螖RST鈮�螖XYZ; SK炉bisects 鈭�RST;YL炉bisect鈭�XYZProve:SK炉鈮�YL炉

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

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

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Write proofs in the form specified by your teacher (two-column form, paragraph) form, or a list of key steps).
Given: $螖 RST 鈮� 螖 XYZ$ ; $\overset{炉}{SK}$ bisects $鈭� RST; \overset{炉}{YL}$ bisect $鈭� XYZ$
Prove: $\overset{炉}{SK} 鈮� \overset{炉}{YL}$