Final answer:
To prove ∠APQR ≅ ∠ATSR, we can use the given information that QR is perpendicular to PT and QPR is similar to ZSTR. By using congruent angles and the transitive property, we can show that angle APQR is congruent to angle ATSR.
Step-by-step explanation:
To prove ∠APQR ≅ ∠ATSR, we can use the given information that QR is perpendicular to PT and QPR is similar to ZSTR. From the given information, we can determine that angle APQ is congruent to angle ATS, and angle QPR is congruent to angle STR. Additionally, we know that angle APQ and angle QRP are supplementary since QR is perpendicular to PT. Therefore, angle APQ is congruent to angle ATP by the vertical angles theorem. Similarly, we can show that angle STR is congruent to angle SRQ. Since angle APQ is congruent to angle ATP and angle STR is congruent to angle SRQ, we can conclude that angle APQR is congruent to angle ATSR by the transitive property of congruence.