Question

Match the reasons with the statements in the proof if the last line of the proof is:

Answer 1

Answer:

Given : S ║ T,

We have to prove that : ∠3 and ∠5 are supplementary

Proof :

Thus, the column proof is as follow,

        Statement                                       Reason

1.   S ║ T                                               1. Given

2. ∠1 and ∠3 are supplementary       2. exterior sides in opposite ray

3. m∠1 + m∠3 = 180°                           3. Definition of supplementary

4. m∠1 = m∠5                                      4. if lines are ║, cor. angles are equal

5. m∠5 + m∠3 = 180°                          5. Substitution

Hence, ∠3 and ∠5 are supplementary.

Note : Since, if the exterior sides are opposite rays, then they always form a straight line.

Answer 2

Answer:

Given : s||t

Exterior sides in opposite rays : ∠5 and ∠7 are supplementary

Definition of supplementary angles : m∠5 + m∠7 = 180°

If lines are ||, corresponding angles are equal : m∠1 = m∠5

Substitution : m∠1 + m∠7 = 180°