Question

Which of the following set is the correct set of corresponding angles for the figure given below?

• A. $\angle PTQ=\angle RSQ$,
  $\angle TQP=\angle SQR$,
  $\angle QPT=\angle QRS$
• B. $\angle PTQ=\angle RSQ$,
  $\angle TQP=\angle SRQ$,
  $\angle QPT=\angle QSR$
• C. $\angle PTQ=\angle RSQ$,
  $\angle TQP=\angle QSR$,
  $\angle QPT=\angle SRQ$
• D. None of the above

Answer 1

The correct option is A $\angle PTQ=\angle RSQ$,

$\angle TQP=\angle SQR$,
$\angle QPT=\angle QRS$
Consider $△TPQ$ and $△SRQ$
Given that
TQ = SQ
PQ = QR
TP = SR
Hence both the triangles are congruent by SSS criterion for congruency of triangles.

By using corresponding parts of congruent triangle criteria, we observe,
$\angle PTQ=\angle RSQ$,
$\angle TQP=\angle SQR$,
$\angle QPT=\angle QRS$