Question

Use the conditional: If $\overline{AB}$and $\overline{CD}$intersect, then $\overrightarrow{AB}$and $\overrightarrow{CD}$intersect.

Given:$m\angle A+m\angle B=180;m\angle C=m\angle B$

What property of equality justifies the statement $m\angle A+m\angle C=180$?

Short answer

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

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.