Question

What statement best fills in the last blank of the proof and completes the sentence: " By the substitution property of equality,..."

Answer 1

A.
`m\angle A=m\angle B`

Explanation:

We have been given that angle A is a right angle and angle B is a right angle. We are asked to choose the correct option that completes the last statement of the proof.

Let us prove that
`m\angle A=m\angle B` step by step.

First blank:

We have been given that
`\angle A \text{ And }\angle B\text{ are right angles}.`.

Second blank:

This means that
`m\angle A=90^o` and
`m\angle B=90^o`

Third blank:

By the definition of right angles a right angle is an angle of exactly 90°.

Last blank:

Substitution property of equality states that if
`a=b\text{ and }b=c\text{ then }a=c`

Hence, by the substitution property of equality
`m\angle A=m\angle B`.

Therefore, the statement
`m\angle A=m\angle B` completes the last blank of the proof and option A is the correct choice.

Answer 2

Since, it is given that angle A is a right angle and angle B is a right angle.

We have to prove that
`m \angle A = m \angle B`

Now, we have to complete the given statement.

It is given that
`\angle A` and
`\angle B` are right angles. This means that
`m \angle A = 90^\circ` and
`m \angle B = 90^\circ` because of the definition of the right angles. By the substitution property of equality
`m \angle A = m \angle B`.