Question

Select the following that are true.Select one or more:a.If a quadrilateral is a square, then it is a rectangle.b.If a quadrilateral is a square, then it is a parallelogram.c.If a quadrilateral is a rhombus, then it is a parallelogram.d.If a quadrilateral is a rectangle, then it is a rhombus.e.If a quadrilateral is a square, then it is a rhombus.f.If a quadrilateral is a parallelogram, then it is a rectangle.

Answer 1

a. One of the properties of squares is all sides are congruent (they have the same length) and this is not a property of rectangles. But the square is a special rectangle since it fits in the properties of rectangles, but rectangles are not squares. In this case, this is TRUE.

b. A parallelogram is a quadrilateral with two pairs of opposite parallel sides and the opposite sides are congruent. The square fits into this description, so this is TRUE.

c. A rhombus has four equal opposite parallel sides, so we can say it fits into the parallelogram definition. This is TRUE.

d. As we said in part a, a rectangle doesn't have all of its sides congruent, but the rhombus does. Then, this is FALSE.

e. Squares have four equal opposite parallel sides, and rhombus too. Then, a square is a rhombus. This is TRUE.

f. Not all parallelograms have the properties of rectangles, then this is FALSE.