Q13. Write proofs in two鈥揷olumn for... [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: Q13. (page 137)

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{JK}$ ; $鈭� 1 鈮� 鈭� 2$
Prove: $\overset{炉}{JG} 鈮� \overset{炉}{MK}$

Short Answer

Expert verified

Statement	Reason
$鈭� 1 鈮� 鈭� 2$	Given
$\overset{炉}{JG} 鈮� \overset{炉}{JM}$	Converse of isosceles theorem
$M$ is the midpoint of $\overset{炉}{JK}$	Given
$\overset{炉}{JM} 鈮� \overset{炉}{MK}$	Midpoint definition
$\overset{炉}{JG} 鈮� \overset{炉}{MK}$	Transitive property

Step by step solution

Step 1. Converse of isosceles theorem.

If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

From the given figure it can be observed that $\overset{炉}{J G}$ is opposite to $鈭� 2$ and $\overset{炉}{J M}$ is opposite to $鈭� 1$ .

As $鈭� 1 鈮� 鈭� 2$ , $\overset{炉}{J G} 鈮� \overset{炉}{J M}$ .

Step 2. Description of step.

Since $M$ is the midpoint of $\overset{炉}{J K}$ , by definition of midpoint

$\overset{炉}{J M} 鈮� \overset{炉}{M K}$

Step 3. Transitive property of congruence.

If $鈭� P 鈮� 鈭� Q$ and $鈭� Q 鈮� 鈭� S$ then $鈭� P 鈮� 鈭� S$ .

Since, $\overset{炉}{J M} 鈮� \overset{炉}{M K}$ and $\overset{炉}{J G} 鈮� \overset{炉}{J M}$ implies that $\overset{炉}{J G} 鈮� \overset{炉}{M K}$ .

Step 4. Two column proof.

Write a two-column proof based on above explanation.

Statement	Reason
$鈭� 1 鈮� 鈭� 2$	Given
$\overset{炉}{J G} 鈮� \overset{炉}{J M}$	Converse of isosceles theorem
$M$ is the midpoint of $\overset{炉}{J K}$	Given
$\overset{炉}{J M} 鈮� \overset{炉}{M K}$	Midpoint definition
$\overset{炉}{J G} 鈮� \overset{炉}{M K}$	Transitive property

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91影视

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{JK}$ ; $鈭� 1 鈮� 鈭� 2$
Prove: $\overset{炉}{JG} 鈮� \overset{炉}{MK}$

Short Answer

Step by step solution

Step 1. Converse of isosceles theorem.

Step 2. Description of step.

Step 3. Transitive property of congruence.

Step 4. Two column proof.

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91影视

Write proofs in two鈥揷olumn form.Given:M is the midpoint of JK炉;鈭�1鈮�鈭�2Prove:JG炉鈮�MK炉

Short Answer

Step by step solution

Step 1. Converse of isosceles theorem.

Step 2. Description of step.

Step 3. Transitive property of congruence.

Step 4. Two column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{JK}$ ; $鈭� 1 鈮� 鈭� 2$
Prove: $\overset{炉}{JG} 鈮� \overset{炉}{MK}$