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Lesson 8-6

Lesson 8-6. Trapezoids. Transparency 8-6. 5-Minute Check on Lesson 8-5. L. LMNO is a rhombus. Find x Find y QRST is a square. Find n if m TQR = 8n + 8. Find w if QR = 5w + 4 and RS = 2(4w – 7). Find QU if QS = 16t – 14 and QU = 6t + 11.

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Lesson 8-6

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  1. Lesson 8-6 Trapezoids

  2. Transparency 8-6 5-Minute Check on Lesson 8-5 L • LMNO is a rhombus. • Find x • Find y • QRST is a square. • Find n if mTQR = 8n + 8. • Find w if QR = 5w + 4 and RS = 2(4w – 7). • Find QU if QS = 16t – 14 and QU = 6t + 11. • 6. What property applies to a square, but not to a rhombus? (8y – 6)° (3x + 12)° 7 M O P 12 (5x – 2)° N Q R 10.25 U 6 T S 65 Standardized Test Practice: A C Opposite sides are congruent Diagonals bisect each other D B D Opposite angles are congruent All angles are right angles Click the mouse button or press the Space Bar to display the answers.

  3. Objectives • Recognize and apply the properties of trapezoids • Solve problems involving medians of trapezoids

  4. Vocabulary • Trapezoid – a quadrilateral with only one pair of parallel sides • Isosceles Trapezoid – a trapezoid with both legs (non parallel sides) congruent • Median – a segment that joins the midpoints of the legs of a trapezoid

  5. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites Trapezoids IsoscelesTrapezoids Rectangles Rhombi Squares

  6. Trapezoids Trapezoid CharacteristicsBases Parallel Legs are not Parallel Leg angles are supplementary (mA + mC = 180, mB + mD = 180) Median is parallel to basesMedian = ½ (base + base)½(AB + CD) base A B legmidpoint legmidpoint median C D base A B Isosceles Trapezoid CharacteristicsLegs are congruent (AC  BD) Base angle pairs congruent (A  B, C  D) Diagonals are congruent (AD  BC) M C D

  7. Example 6-2a The top of this work station appears to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Each pair of base angles is congruent, so the legs are the same length. Answer: Both trapezoids are isosceles.

  8. Example 6-2b The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Answer: yes

  9. DEFG is an isosceles trapezoid with median Find DG if and Answer: Example 6-4a Theorem 8.20 Substitution Multiply each side by 2. Subtract 20 from each side.

  10. DEFG is an isosceles trapezoid with median Find , and if and Example 6-4c Since EF // DG, 1 and 3 are supplementary Because this is an isosceles trapezoid, 1  2 and 3  4 Substitution Combine like terms. Divide each side by 9. Answer: If x = 20, then m1 = 65° and 3 = 115°. Because 1  2 and 3  4, 2 = 65° and 4 = 115°

  11. WXYZ is an isosceles trapezoid with median a. Answer: b. Answer: Because Example 6-4e

  12. Quadrilateral Characteristics Summary Convex Quadrilaterals 4 sided polygon 4 interior angles sum to 360 4 exterior angles sum to 360 Parallelograms Trapezoids Bases Parallel Legs are not Parallel Leg angles are supplementary Median is parallel to basesMedian = ½ (base + base) Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangles Rhombi IsoscelesTrapezoids All sides congruent Diagonals perpendicular Diagonals bisect opposite angles Angles all 90° Diagonals congruent Legs are congruent Base angle pairs congruent Diagonals are congruent Squares Diagonals divide into 4 congruent triangles

  13. Summary & Homework • Summary: • In an isosceles trapezoid, both pairs of base angles are congruent and the diagonals are congruent. • The median of a trapezoid is parallel to the bases and its measure is one-half the sum of the measures of the bases • Homework: • pg 442-444; 10, 13-16, 22-25

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