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ABCD is a quadrilateral because it has four sides.

It is a trapezoid because AB and DC appear parallel and AD and BC appear nonparallel. Classifying Quadrilaterals. LESSON 6-1. Additional Examples. Judging by appearance, classify ABCD in as many ways as possible. ABCD is a quadrilateral because it has four sides.

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ABCD is a quadrilateral because it has four sides.

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  1. It is a trapezoid because AB and DC appear parallel and AD and BC appear nonparallel. Classifying Quadrilaterals LESSON 6-1 Additional Examples Judging by appearance, classify ABCD in as many ways as possible. ABCD is a quadrilateral because it has four sides. Quick Check

  2. Graph quadrilateral QBHA. First, find the slope of each side. slope of QB = slope of BH = slope of HA = slope of QA = 4 – 4 –4 – 10 9 – 9 8 – (–2) 4 – 9 10 – 8 9 – 4 –2 – (–4) 5 2 5 2 = = = = – 0 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 Determine the most precise name for the quadrilateral with vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4).

  3. 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 (continued) 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. Because QB = HA, QBHA is an isosceles trapezoid. Quick Check

  4. If lines are parallel, then interior angles on the same side of a transversal are supplementary. m R + m S = 180 Draw quadrilateral RSTU. Label R and S. RSTU is a parallelogram. Given ST || RU Definition of parallelogram Classifying Quadrilaterals LESSON 6-1 Additional Examples In parallelogram RSTU, mR = 2x – 10 and m S = 3x + 50. Find x.

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

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