Chapter 2: Q5 (page 49)

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Given: $m ∠ A + m ∠ B = 180; m ∠ C = m ∠ B$
What property of equality justifies the statement $m ∠ A + m ∠ C = 180$ ?

Short Answer

Expert verified

The required property is the substitution property.

Step by step solution

Step 1. Observe the given statement.

The provided statement states that the measurement of $∠ A$ and $∠ C$ is equal to 180 and it is also true for the angles A and B so, in statement $m ∠ A + m ∠ B = 180$ , the $m ∠ B$ can be replaced with $m ∠ C$ because the measurement of $∠ C$ is the same as the measurement of $∠ B$ .

Step 2. Identify the property.

The provided statement is justified with the help of a substitute so this operation can be done with the help of substitution property.

Step 3. Make the conclusion.

As substitution property helps in justification so it is the required property.

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Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Given: $m ∠ A + m ∠ B = 180; m ∠ C = m ∠ B$
What property of equality justifies the statement $m ∠ A + m ∠ C = 180$ ?

Short Answer

Step by step solution

Step 1. Observe the given statement.

Step 2. Identify the property.

Step 3. Make the conclusion.

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Use the conditional: If AB¯and CD¯intersect, then AB→and CD→intersect.Given:m∠A+m∠B=180;m∠C=m∠BWhat property of equality justifies the statement m∠A+m∠C=180?

Short Answer

Step by step solution

Step 1. Observe the given statement.

Step 2. Identify the property.

Step 3. Make the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Given: $m ∠ A + m ∠ B = 180; m ∠ C = m ∠ B$
What property of equality justifies the statement $m ∠ A + m ∠ C = 180$ ?