1. GEOMETRY HELP 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 Quadrilaterals LESSON 6-1 Additional Examples

2. GEOMETRY HELP 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) 5252 = 9 – 9 8 – (–2) = 0 4 – 9 10 – 8 = – 5252 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 Quadrilaterals LESSON 6-1 Additional Examples

3. GEOMETRY HELP 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 Quadrilaterals LESSON 6-1 Additional Examples Quick Check

4. GEOMETRY HELP 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 parallelogramST || RU m R + m S = 180 If lines are parallel, then interior angles on the same side of a transversal are supplementary. Classifying Quadrilaterals LESSON 6-1 Additional Examples

5. GEOMETRY HELP (continued) Subtract 40 from each side. 5x = 140 5x + 40 = 180 Simplify. x = 28 Divide each side by 5. (2x – 10) + (3x + 50) = 180Substitute 2x – 10 for m R and 3x + 50 for m S. Classifying Quadrilaterals LESSON 6-1 Additional Examples Quick Check