In the diagram shown, parallelogram mnpq is shown with points located on it's such that mu ≅ sp and rn ≅ qt.

prove that rstu must be a parallelogram.

See explanation

Step-by-step explanation:

MNPQ is a parallelogram. Then

By segment addition postulate,

Given that MU ≅ SP and RN ≅ QT, then and

Consider triangles QUT and NSR. In these triangles,

- proven; - given; - as opposite ngles of parallelogram MNPQ.

By SAS postulate, triangles QUT and NSR are congruent. Then

Consider triangles MRU and PTS. In these triangles,

- proven; - given; - as opposite ngles of parallelogram MNPQ.

By SAS postulate, triangles MRU and TPS are congruent. Then

In quadrilateral RSTU, and Since opposite sides of the quadrilateral are congruent, the quadrilateral is a parallelogram.

x = 0.5 or x = 4.5

step-by-step explanation:

Yes, two vertical lines can be complementary