Question

question 5
using the given information below, which test for parallelograms proves that qrst is a parallelogram?
image of quadrilateral qrst with angles: q=140°, r=40°, s=140°, t=40°
opposite sides are congruent
opposite sides are parallel
all pairs of consecutive angles are supplementary
one pair of opposite sides is parallel and congruent

Explanation:

Step1: Analyze consecutive angles

Check consecutive angles: \( \angle Q = 140^\circ \), \( \angle R = 40^\circ \), sum \( 140 + 40 = 180^\circ \). \( \angle R = 40^\circ \), \( \angle S = 140^\circ \), sum \( 40 + 140 = 180^\circ \). \( \angle S = 140^\circ \), \( \angle T = 40^\circ \), sum \( 140 + 40 = 180^\circ \). \( \angle T = 40^\circ \), \( \angle Q = 140^\circ \), sum \( 40 + 140 = 180^\circ \).

Step2: Match with parallelogram test

The test "All pairs of consecutive angles are supplementary" fits, as consecutive angles sum to \( 180^\circ \) (supplementary), proving it's a parallelogram. Other options: "Opposite sides congruent" needs side info (not given), "Opposite sides parallel" needs slope/parallel info (not given), "One pair opposite sides parallel and congruent" needs side info (not given).

Answer:

All pairs of consecutive angles are supplementary