Question

QS∥PT. Complete the proof that m∠P+m∠T=m∠RQT without using the Triangle Angle Sum Theorem.

Answer 1

Solution:

Given the figure;

$\bar{QS}||\bar{PT}................\text{ Given}$

Then;

$\angle P\cong\angle RQS....................\text{ Corresponding angle theorem}$$\angle T\cong\angle SQT...............\text{ Alternate interior angles theorem}$$m\angle RQS+m\angle SQT=m\angle RQT..........\text{ Additive property of angle measure}$$m\angle P+m\angle T=m\angle RQT..........\text{ Substitution}$

CORRECT ANSWER: Corresponding Angles Theorem