Question

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

Answer 1

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