Samantha has cut a pastry into four parts. Suppose PS is parallel to RT and T is the midpoint of PR. Determine whether SPT is congruent to QRT

Question

Answer 1

Suppose you meant PQ is parallel to SR

angle RPQ = angle SRP are congruent alternate interior angles

angle STR = angle PTQ are congruent vertical angles

PT = TR is given as T is the midpoint of PR

by ASA, triangle STR = triangle PTQ

THEN, by CPCTC:

PT=ST

RT = TQ

angle STP = angle RTQ are congruent vertical angles

By SAS,

SPT is congruent to QRT