Answer:
Step-by-step explanation:
Chords QP and RS are congruent
Chords PS and QR are congruent
Step-by-step explanation:
see the attached figure to better understand the problem
Part 1)
we know that
m∠PTQ≅m∠STR -----> by vertical angles
so
Triangles PTQ and STR are congruent by SAS postulate
because
PT≅ST ----> the radius of circle
QT≅RT ----> the radius of circle
m∠PTQ≅m∠STR
therefore
Chords QP and RS are congruent
Part 2)
we know that
m∠PTS≅m∠QTR -----> by vertical angles
so
Triangles PTS and QTR are congruent by SAS postulate
because
PT≅QT ----> the radius of circle
ST≅RT ----> the radius of circle
m∠PTS≅m∠QTR
therefore
Chords PS and QR are congruent
