Chapter 6: Q10. (page 207)

Write proofs in two-column form.
Given: $\bar{V Y} ⊥ \bar{Y Z}$ . Prove: $∠ V X Z$ is an obtuse angle.

Short Answer

Expert verified

Statement	Reason
1. $∠ Y + ∠ Z + ∠ Y X Z = 180$	Angle sum property
2. $∠ Y X Z + ∠ V X Z = 180$	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 $\bar{V Y} ⊥ \bar{Y Z}$ therefore, $∠ X Y Z = ∠ Y = 90$ .

The sum of the angles of triangle will be:

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

Since $∠ Z > 90$ , therefore $∠ Y X Z < 90$ .

Step 3. Prove the statement

From the figure

Use linear angle property as follows:

$∠ Y X Z + ∠ V X Z = 180$

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

Therefore, $∠ V X Z$ is an obtuse angle.

Hence proved.

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Write proofs in two-column form.
Given: $\bar{V Y} ⊥ \bar{Y Z}$ . Prove: $∠ V X Z$ 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

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Write proofs in two-column form.Given: VY¯⊥YZ¯. Prove: ∠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

Pure Maths

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $\bar{V Y} ⊥ \bar{Y Z}$ . Prove: $∠ V X Z$ is an obtuse angle.