Question

proving the congruent supplements theorem
given: ∠1 and ∠2 are supplements, and ∠3 and ∠2 are supplements.
prove: ∠1≅∠3
complete the missing parts of the paragraph proof.
by the definition of blank angles, the sum of the measures of angles 1 and 2 is 180 degrees. likewise, the sum of the measures of angles blank is 180 degrees. by the blank property, m∠1 + m∠2 = m∠3 + m∠2. subtract the measure of angle blank from each side. you get m∠1 = m∠3, or ∠1≅∠3, by the definition of congruence.

Explanation:

Step1: Recall supplement - angle definition

By the definition of supplementary angles, the sum of the measures of angles 1 and 2 is 180 degrees. Also, since ∠3 and ∠2 are supplements, the sum of the measures of angles 3 and 2 is 180 degrees.

Step2: Use the transitive property

We know that if \(m\angle1 + m\angle2=180\) and \(m\angle3 + m\angle2 = 180\), by the transitive property, \(m\angle1 + m\angle2=m\angle3 + m\angle2\).

Step3: Subtract the common - angle measure

Subtract the measure of angle 2 from each side of the equation \(m\angle1 + m\angle2=m\angle3 + m\angle2\). Using the subtraction property of equality, we get \(m\angle1=m\angle3\). Then, by the definition of congruence, \(\angle1\cong\angle3\).

Answer:

1. Supplementary
2. 3 and 2
3. Transitive
4. 2