Question

in a trapezoid, the measure of the consecutive angles next to the longer base are
a. supplementary
b. perpendicular
c. complementary
d. congruent

a square is a parallelogram that is both a ____ and a ____.
a. rectangle, polygon
b. rhombus, polygon
c. quadrilateral, rectangle
d. rectangle, rhombus

in a parallelogram, opposite sides are both parallel and ______.
a. congruent
b. obtuse
c. perpendicular
d. supplementary

if one pair of opposite sides of a quadrilateral are both parallel and congruent, what can you conclude?
a. the quadrilateral is a trapezoid
b. the quadrilateral is a rhombus
c. the quadrilateral is a rectangle
d. the quadrilateral is a parallelogram

Explanation:

1. In a trapezoid, the bases are parallel. By the property of parallel - lines, consecutive angles next to any base (including the longer base) are supplementary since they are same - side interior angles.
2. A square has all the properties of a rectangle (four right angles) and a rhombus (all sides are equal). A square is a parallelogram that is both a rectangle and a rhombus.
3. One of the defining properties of a parallelogram is that opposite sides are parallel and congruent.
4. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram according to the parallelogram criterion.

Answer:

1. a. supplementary
2. d. rectangle, rhombus
3. a. congruent
4. d. The quadrilateral is a parallelogram