Question

If quadrilateral PQRS is a parallelogram, line segment QR is ≅ to line segment QT, and m∠TQR=60°, which angles are congruent to ∠S? Select all that apply.

a.) ∠P
b.) ∠PQR
c.) ∠RQT
d.) ∠QRT
e.) ∠SRQ
f.) ∠TQR

Answer 1

From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)

b, c, d, and f are true

The opposite angles of a parallelogram are congruent (b)

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)

Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)

Transitive property, like c (f)