Q10. Write proofs in two-column form.... [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 6: Q10. (page 207)

Write proofs in two-column form.
Given: $\overset{炉}{V Y} 鈯� \overset{炉}{Y Z}$ . Prove: $鈭� V X Z$ is an obtuse angle.

Short Answer

Expert verified

Statement	Reason
1. $鈭� Y + 鈭� Z + 鈭� Y X Z = 180$	Angle sum property
2. $鈭� Y X Z + 鈭� V X Z = 180$	Linear angles

Step by step solution

Step 1. Angles property of a triangle

The sum of the angles of a triangle is 180. If an angle is greater than 90 then it is an obtuse angle.

Step 2. Use the angle sum property and find the angle YXZ

Since $\overset{炉}{V Y} 鈯� \overset{炉}{Y Z}$ therefore, $鈭� X Y Z = 鈭� Y = 90$ .

The sum of the angles of triangle will be:

role="math" localid="1637852883028" $\begin{matrix} 鈭� Y + 鈭� Z + 鈭� Y X Z = 180 \\ 鈭� Z + 鈭� Y X Z = 180 鈭� 鈭� Y \\ 鈭� Z + 鈭� Y X Z = 180 鈭� 90 \\ 鈭� Z + 鈭� Y X Z = 90 \end{matrix}$

Since $鈭� Z > 90$ , therefore $鈭� Y X Z < 90$ .

Step 3. Prove the statement

From the figure

Use linear angle property as follows:

$鈭� Y X Z + 鈭� V X Z = 180$

Since $鈭� Y X Z < 90$ therefore from equation (1) $鈭� V X Z > 90$ .

Therefore, $鈭� V X Z$ is an obtuse angle.

Hence proved.

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91影视

Write proofs in two-column form.
Given: $\overset{炉}{V Y} 鈯� \overset{炉}{Y Z}$ . Prove: $鈭� V X Z$ is an obtuse angle.

Short Answer

Step by step solution

Step 1. Angles property of a triangle

Step 2. Use the angle sum property and find the angle YXZ

Step 3. Prove the statement

One App. One Place for Learning.

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91影视

Write proofs in two-column form.Given: VY炉鈯�YZ炉. Prove: 鈭�VXZ is an obtuse angle.

Short Answer

Step by step solution

Step 1. Angles property of a triangle

Step 2. Use the angle sum property and find the angle YXZ

Step 3. Prove the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Discrete Mathematics

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $\overset{炉}{V Y} 鈯� \overset{炉}{Y Z}$ . Prove: $鈭� V X Z$ is an obtuse angle.