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: Q7. (page 149)

Given: $\overset{炉}{LF} 鈮� \overset{炉}{KF}; \overset{炉}{LA} 鈮� \overset{炉}{KA}$
Prove: $\overset{炉}{LJ} 鈮� \overset{炉}{KJ}$
a. List the key steps of a proof.
b. Write a proof in two-column form.

Short Answer

Expert verified

$螖 LAF 鈮� 螖 KAF$	SSS property
$鈭� LAF 鈮� 鈭� KAF$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 LAJ 鈮� 螖 KAJ$	SAS postulate
$\overset{炉}{LJ} 鈮� \overset{炉}{KJ}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Statements	Reason
$\overset{炉}{LF} 鈮� \overset{炉}{KF}; \overset{炉}{LA} 鈮� \overset{炉}{KA}$	Given
$\overset{炉}{AF} 鈮� \overset{炉}{AF}$	Reflexive property
$螖 LAF 鈮� 螖 KAF$	SSS property
$鈭� LAF 鈮� 鈭� KAF$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 LAJ 鈮� 螖 KAJ$	SAS postulate
$\overset{炉}{LJ} 鈮� \overset{炉}{KJ}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Part a. Step 1. Description of step.

Consider $螖 L A F$ and $螖 K A F$ , $\overset{炉}{A F} 鈮� \overset{炉}{A F}$ by reflexive property. Also, by given information, $\overset{炉}{L F} 鈮� \overset{炉}{K F}$ and $\overset{炉}{L A} 鈮� \overset{炉}{K A}$ . Therefore, by SSS postulate, $螖 L A F 鈮� 螖 K A F$ .

Part a. Step 2. Description of step.

As $螖 L A F 鈮� 螖 K A F$ , by corresponding parts of congruent triangles, $鈭� L A F 鈮� 鈭� K A F$ .

Part a. Step 3. Description of step.

Consider $螖 L A J$ and $螖 K A J$ , $\overset{炉}{L A} 鈮� \overset{炉}{K A}$ , $\overset{炉}{A F} 鈮� \overset{炉}{A F}$ and $鈭� L A F 鈮� 鈭� K A F$ , then by SAS postulate, $螖 L A J 鈮� 螖 K A J$ .

Part a. Step 4. Description of step.

As $螖 L A J 鈮� 螖 K A J$ , by corresponding parts of congruent triangles, $\overset{炉}{L J} 鈮� \overset{炉}{K J}$ .

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

Make a list of key steps of a proof.

$螖 L A F 鈮� 螖 K A F$	SSS property
$鈭� L A F 鈮� 鈭� K A F$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 L A J 鈮� 螖 K A J$	SAS postulate
$\overset{炉}{L J} 鈮� \overset{炉}{K J}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Part b. Step 1. Description of step.

Consider $螖 L A F$ andwidth="115" height="23" role="math">螖KAF,AF炉鈮�AF炉 by reflexive property. Also, by given information, $\overset{炉}{L F} 鈮� \overset{炉}{K F}$ and $\overset{炉}{L A} 鈮� \overset{炉}{K A}$ . Therefore, by SSS postulate, $螖 L A F 鈮� 螖 K A F$ .

Part b. Step 2. Description of step.

As $螖 L A F 鈮� 螖 K A F$ , by corresponding parts of congruent triangles, $鈭� L A F 鈮� 鈭� K A F$ .

Part b. Step 3. Description of step.

Consider $螖 L A J$ and $螖 K A J, \overset{炉}{L A} 鈮� \overset{炉}{K A}, \overset{炉}{A F} 鈮� \overset{炉}{A F}$ and $鈭� L A F 鈮� 鈭� K A F$ , then by SAS postulate, $螖 L A J 鈮� 螖 K A J$ .

Part b. Step 4. Description of step.

As $螖 L A J 鈮� 螖 K A J$ , by corresponding parts of congruent triangles, $\overset{炉}{L J} 鈮� \overset{炉}{K J}$ .

Part b. Step 5. Two-column proof.

Write a two-column proof of the above explanation.

Statements	Reason
$\overset{炉}{L F} 鈮� \overset{炉}{K F}; \overset{炉}{L A} 鈮� \overset{炉}{K A}$	Given
$\overset{炉}{A F} 鈮� \overset{炉}{A F}$	Reflexive property
$螖 L A F 鈮� 螖 K A F$	SSS property
$鈭� L A F 鈮� 鈭� K A F$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 L A J 鈮� 螖 K A J$	SAS postulate
$\overset{炉}{L J} 鈮� \overset{炉}{K J}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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91影视

Given: $\overset{炉}{LF} 鈮� \overset{炉}{KF}; \overset{炉}{LA} 鈮� \overset{炉}{KA}$
Prove: $\overset{炉}{LJ} 鈮� \overset{炉}{KJ}$
a. List the key steps of a proof.
b. Write a proof in two-column 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:LF炉鈮�KF炉;LA炉鈮�KA炉Prove:LJ炉鈮�KJ炉a. List the key steps of a proof.b. Write a proof in two-column 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

Mechanics Maths

Probability and Statistics

Geometry

Calculus

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{LF} 鈮� \overset{炉}{KF}; \overset{炉}{LA} 鈮� \overset{炉}{KA}$
Prove: $\overset{炉}{LJ} 鈮� \overset{炉}{KJ}$
a. List the key steps of a proof.
b. Write a proof in two-column form.