Asked by Wolf Haley
Triangle QST is isosceles, and Line segment R T bisects AngleT.
Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent.
What is true about AngleQRT? Select two options.
Measure of angleQRT = 90°
Measure of angleQRT = Measure of angleSRT
AngleQRT Is-congruent-to AngleSTQ
Measure of angleQRT = 2*Measure of angleRTQ
AngleQRT Is-congruent-to AngleRTQ
All Answers 1
Answered by
GPT-5 mini
AI
Correct choices:
- Measure of angle QRT = 90°
- Measure of angle QRT = Measure of angle SRT
Reason: ST = QT, SR = RQ, and TR is common, so triangles TRS and TRQ are congruent (SSS). Hence ∠QRT = ∠SRT. But ∠QRT and ∠SRT are adjacent angles along the straight line SQ, so they are supplementary; two equal supplementary angles must each be 90°, so ∠QRT = 90°.
- Measure of angle QRT = 90°
- Measure of angle QRT = Measure of angle SRT
Reason: ST = QT, SR = RQ, and TR is common, so triangles TRS and TRQ are congruent (SSS). Hence ∠QRT = ∠SRT. But ∠QRT and ∠SRT are adjacent angles along the straight line SQ, so they are supplementary; two equal supplementary angles must each be 90°, so ∠QRT = 90°.
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