Always, Sometimes, Never

Perpendicular lines form complementary vertical angles.

Never. Perpendicular lines form supplementary vertical angles because each angle formed by perpendicular lines are 90˚

In a right scalene triangle, the non-right angles are supplementary.

Never. The sum of all 3 angles in a triangle adds up 180˚, not 2.

It three points are coplanar, then they are also collinear.

Sometimes. A plane is an infinite series of points, so not all of them are collinear.

If two angles are supplementary, then they are adjacent.

Sometimes. Any angles that add up to 180˚ are supplementary. They don't have to be right next to each other.

If two parallel lines are intersected in the same plane by a 3rd line, then the alternate interior angles are supplementary.

Sometimes. Since the alternate interior angles are always congruent when there are parallel lines, the only way this can be possible is if the transversal is perpendicular to the parallel lines to make them both 90˚.

If a line intersects a segment at the segment's midpoint, then it must be the perpendicular bisector of the segment.

Sometimes. The line could intersect at a segment's midpoint at any angle, not always making it perpendicular.

If 2 lines are cut by a transversal, then the alternate interior angles are congruent.

Sometimes. They are only congruent if the 2 lines are parallel.

In quadrilateral EFGH, if EF is congruent to GH, then the quadrilateral is a parallelogram.

Sometimes. Those two lines can be congruent, but not parallel. There is not enough information to determine if it is a parallelogram even though their opposite sides are congruent.

In a quadrilateral, if the diagonals are congruent, then the quadrilateral is a rectangle.

Sometimes. Trapezoids also have congruent diagonals.

If ABCD is an isosceles trapezoid, then AB is parallel to CD

Sometimes. Trapezoids have 1 pair of parallel sides, but it does not have to be horizontal

In a quadrilateral, if two angles are supplementary, then the quadrilateral is a parallelogram.

Sometimes. Two angles can be supplementary in any quadrilateral.

In ∆MNP, if m∠M = 60˚ and MN is congruent to MP, then the triangle is equilateral.

Always

If ABCD is a square, then it must be a rhombus.

Always. A square is always a rhombus because all of their sides are congruent and their diagonals are perpendicular bisectors of each other.

In ∆TOP, if ∠O is congruent to ∠P, then the triangle is isosceles.

Always. An isosceles triangle has two congruent angles because they have two congruent sides.

If two lines are parallel, then they are coplanar.

Always. There is a flat surface that can always cover parallel lines at any angle.