Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
5. Properties of Trapezoids and Kites
Continue to next subchapter

Exercise 10 Page 402

Recall the classification of quadrilaterals.

Quadrilateral, see solution.

Practice makes perfect

We are given the following diagram and asked to given the most specific name for this quadrilateral.

Let's recall the definitions of different types of quadrilaterals.

Quadrilateral Definition
Parallelogram Both pairs of opposite sides are parallel.
Rhombus Parallelogram with four congruent sides.
Rectangle Parallelogram with four right angles.
Square Parallelogram with four congruent sides and four right angles.
Trapezoid Quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid Trapezoid with legs that are congruent.
Kite Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

Now, we can go through each of them and see whether our quadrilateral meets the description.

Quadrilateral Does CDEF meet the definition? Reasoning
Parallelogram No The opposite sides are not marked as parallel.
Rhombus No There are only two congruent sides, not four.
Rectangle No The angles seem to be right angles, but they are not marked as such.
Square No Not all sides are congruent and the measures of the angles are unknown.
Trapezoid No None of the sides are marked as parallel.
Isosceles Trapezoid No It is not a trapezoid.
Kite No One pair of opposite sides is congruent.

As we can see, we do not have enough information to specify CDEF as some kind of quadrilateral. All we know for sure is that CDEF has four sides and four vertices, so the most specific name we can give it is a quadrilateral.