GEOMETRYHELP

ABCD is a quadrilateral because it has four sides.

Judging by appearance, classify ABCD in as many ways as possible.

It is a trapezoid because AB and DC appear parallel and AD and BC appear nonparallel.

Quick Check

Classifying QuadrilateralsLESSON 6-1

Additional Examples

GEOMETRYHELP

Determine the most precise name for the quadrilateral with vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4).

Graph quadrilateral QBHA.

First, find the slope of each side.

slope of QB = slope of BH = slope of HA = slope of QA = 9 – 4 –2 – (–4)

52= 9 – 9

8 – (–2) = 0 4 – 9 10 – 8 = – 5

2 4 – 4 –4 – 10 = 0

BH is parallel to QA because their slopes are equal. QB is not parallel to HA because their slopes are not equal.

Classifying QuadrilateralsLESSON 6-1

Additional Examples

GEOMETRYHELP

Because QB = HA, QBHA is an isosceles trapezoid.

One pair of opposite sides are parallel, so QBHA is a trapezoid.

Next, use the distance formula to see whether any pairs of sides are congruent.

(continued)

QB = ( –2 – ( –4))2 + (9 – 4)2 = 4 + 25 = 29

HA = (10 – 8)2 + (4 – 9)2 = 4 + 25 = 29

BH = (8 – (–2))2 + (9 – 9)2 = 100 + 0 = 10

QA = (– 4 – 10)2 + (4 – 4)2 = 196 + 0 = 14

Classifying QuadrilateralsLESSON 6-1

Additional Examples

Quick Check

GEOMETRYHELP

In parallelogram RSTU, m R = 2x – 10 and m S = 3x + 50. Find x.

Draw quadrilateral RSTU. Label R and S.

RSTU is a parallelogram. Given

Definition of parallelogram ST || RU

m R + m S = 180 If lines are parallel, then interior angles on the same side of a transversal are supplementary.

Classifying QuadrilateralsLESSON 6-1

Additional Examples

GEOMETRYHELP

(continued)

Subtract 40 from each side.5x = 140

5x + 40 = 180 Simplify.

x = 28 Divide each side by 5.

(2x – 10) + (3x + 50) = 180 Substitute 2x – 10 for m R and 3x + 50 for m S.

Classifying QuadrilateralsLESSON 6-1

Additional Examples

Quick Check