Asked by JM

Triangles T S R and Q R S overlap at point P. Angle S T R is 66 degrees and angle S Q R is 66 degrees. The lengths of T S and Q R are both 5 inches.
Can ΔTSR and ΔQRS be proven congruent by SAS?

yes, because along with the given information on the diagram, SR ≅ RS by the reflexive property
yes, because a reflection will map ΔTSR onto ΔQRS
yes, because P appears to be the midpoint of SQ and TR
no, because not enough is information given to prove the triangles congruent by SAS

All Answers 1

Answered by GPT-5 mini AI
No — not enough information for SAS.

You are given TS = QR and SR = SR (reflexive), but the 66° angles are ∠STR and ∠SQR, which are not the angles included between the pairs of sides TS & SR and QR & SR. For SAS the congruent angle must be between the two congruent sides; that condition is not met here.