14 Explain why consecutive angles in a parallelogram are supplementary.
15 Consecutive angles are formed by two parallel lines cut by a transversal. These angle pairs are classified as same-side interior angles and same-side interior angles are supplementary when two parallel lines are cut by a transversal.
16 Based on the markings, decide whether each figure must be a parallelogram.
17 b. No; the diagonals do not necessarily bisect each other. a. Yes; both pairs of alternate interior angles are congruent, therefore both pairs of opposite sides are parallel.b. No; the diagonals do not necessarily bisect each other.
18 Find the values of x and y for the parallelogram below.
26 True or False? a. The opposite sides of a rectangle are congruent. b. The diagonals of a rectangle are always perpendicular.c. The diagonals of a rectangle bisect each other.d. The opposite angles of a rectangle are both congruent and supplementary.
27 a. True; a rectangle is a parallelogram and the opposite sides of a parallelogram are congruent b. False; unless the rectangle is a square, the diagonals are not perpendicular.c. True; a rectangle is a parallelogram and the diagonals of a parallelogram bisect each other.d. True; all four angles in a rectangle are 90 degrees, therefore the opposite angles are both congruent and supplementary.
28 Determine if the following diagrams are rectangles. Justify your answer. b.
29 a. No; the diagonals are not necessarily congruent. b. Yes; the diagonals are congruent.
30 Find the value of x for the following rectangle and then find the length of each diagonal.