Q14. 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: Q14. (page 137)

Write proofs in two鈥揷olumn form.
Given: $\overset{炉}{XY} 鈮� \overset{炉}{XZ};$
Prove: $鈭� 3 鈮� 鈭� 5$

Short Answer

Expert verified

Statement	Reason
$\overset{炉}{XY} 鈮� \overset{炉}{XZ}$	Given
$鈭� 3 鈮� 鈭� 4$	Isosceles triangle theorem
$鈭� 4 鈮� 鈭� 5$	Vertically opposite angles
$鈭� 3 鈮� 鈭� 5$	Transitive property of congruence

Step by step solution

Step 1. Apply isosceles triangle theorem.

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

From the figure it can be observed that, $\overset{炉}{X Y} 鈮� \overset{炉}{X Z}$ .

Therefore, $鈭� 3 鈮� 鈭� 4$ .

Step 2. Vertically opposite angles.

From thefigure it can be observed that, $鈭� 4 and 鈭� 5$ are vertically opposite angles.

Therefore,width="68">鈭�4鈮�鈭�5

Step 3. Transitive property of congruence.

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

As $鈭� 3 鈮� 鈭� 4$ and $鈭� 4 鈮� 鈭� 5$ , $鈭� 3 鈮� 鈭� 5$ .

Therefore, $鈭� 3 鈮� 鈭� 5$ .

Step 4. Two column proof.

Write a two-column proof based on above explanation.

Statement	Reason
$\overset{炉}{X Y} 鈮� \overset{炉}{X Z}$	Given
$鈭� 3 鈮� 鈭� 4$	Isosceles triangle theorem
$鈭� 4 鈮� 鈭� 5$	Vertically opposite angles
$鈭� 3 鈮� 鈭� 5$	Transitive property of congruence

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91影视

Write proofs in two鈥揷olumn form.
Given: $\overset{炉}{XY} 鈮� \overset{炉}{XZ};$
Prove: $鈭� 3 鈮� 鈭� 5$

Short Answer

Step by step solution

Step 1. Apply isosceles triangle theorem.

Step 2. Vertically opposite angles.

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:XY炉鈮�XZ炉;Prove:鈭�3鈮�鈭�5

Short Answer

Step by step solution

Step 1. Apply isosceles triangle theorem.

Step 2. Vertically opposite angles.

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

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write proofs in two鈥揷olumn form.
Given: $\overset{炉}{XY} 鈮� \overset{炉}{XZ};$
Prove: $鈭� 3 鈮� 鈭� 5$