Chapter 6: Q11. (page 207)

Write proofs in two-column form.
Given: The diagram. Prove: $m ∠ 1 > m ∠ 4$

Short Answer

Expert verified

Statement	Reasons
1. , $m ∠ 1 > m ∠ 2$ , $m ∠ 2 > m ∠ 3$	Exterior angle theorem
2. $m ∠ 1 > m ∠ 3$	Property of Inequality If and then .
3. $m ∠ 3 = m ∠ 4$	Vertically opposite angle.
4. $m ∠ 1 > m ∠ 4$	Substitution property

Step by step solution

Step 1. Draw diagram and define exterior angle inequality theorem

Two triangles as shown below are the given triangles.

The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

Therefore, from the figure $m ∠ 1 > m ∠ 2$ and $m ∠ 2 > m ∠ 3$ .

Step 2. Property of inequality and use vertically opposite angle property

If $a > b$ and $b > c$ then $a > c$ . Since $m ∠ 1 > m ∠ 2$ and $m ∠ 2 > m ∠ 3$ , therefore $m ∠ 1 > m ∠ 3$ .

The vertically opposite angles are always equal.

Since $∠ 3$ and $∠ 4$ are vertically opposite angles, therefore $m ∠ 3 = m ∠ 4$ .

Step 3. Prove the statement

Since $m ∠ 3 = m ∠ 4$ and $m ∠ 1 > m ∠ 3$ therefore by substitution property role="math" localid="1637858624737" $m ∠ 1 > m ∠ 4$ .

Hence proved.

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Write proofs in two-column form.
Given: The diagram. Prove: $m ∠ 1 > m ∠ 4$

Short Answer

Step by step solution

Step 1. Draw diagram and define exterior angle inequality theorem

Step 2. Property of inequality and use vertically opposite angle property

Step 3. Prove the statement

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Write proofs in two-column form.Given: The diagram. Prove: m∠1>m∠4

Short Answer

Step by step solution

Step 1. Draw diagram and define exterior angle inequality theorem

Step 2. Property of inequality and use vertically opposite angle property

Step 3. Prove the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Statistics

Calculus

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: The diagram. Prove: $m ∠ 1 > m ∠ 4$