Transcript Document
Lesson 8-6 Trapezoids Transparency 8-6 5-Minute Check on Lesson 8-5 LMNO is a rhombus. 1. Find x 2. Find y L (8y – 6)° (3x + 12)° 7 O 12 M P (5x – 2)° QRST is a square. N 3. Find n if mTQR = 8n + 8. 10.25 Q 4. Find w if QR = 5w + 4 and RS = 2(4w – 7). 5. Find QU if QS = 16t – 14 and QU = 6t + 11. 6. Standardized Test Practice: not to a rhombus? R U 6 65 T S What property applies to a square, but A Opposite sides are congruent C Diagonals bisect each other B Opposite angles are congruent D All angles are right angles Click the mouse button or press the Space Bar to display the answers. Objectives • Recognize and apply the properties of trapezoids • Solve problems involving medians of trapezoids 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 Polygon Hierarchy Polygons Quadrilaterals Parallelograms Rectangles Rhombi Squares Kites Trapezoids Isosceles Trapezoids Trapezoids Trapezoid Characteristics A Bases Parallel Legs are not Parallel Leg angles are supplementary (mA + mC = 180, mB + mD = 180) Median is parallel to bases Median = ½ (base + base) leg midpoint base median C ½(AB + CD) B leg midpoint D base A B Isosceles Trapezoid Characteristics Legs are congruent (AC BD) Base angle pairs congruent (A B, C D) Diagonals are congruent (AD BC) M C D 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. The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Answer: yes DEFG is an isosceles trapezoid with median DG if and Find Theorem 8.20 Substitution Multiply each side by 2. Subtract 20 from each side. Answer: DEFG is an isosceles trapezoid with median Find , and if and 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 m1 = 65° and 3 = 115°. Because 1 2 and 3 4, 2 = 65° and 4 = 115° WXYZ is an isosceles trapezoid with median a. Answer: b. Answer: Because Quadrilateral Characteristics Summary Convex Quadrilaterals Parallelograms 4 sided polygon 4 interior angles sum to 360 4 exterior angles sum to 360 Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangles Trapezoids Bases Parallel Legs are not Parallel Leg angles are supplementary Median is parallel to bases Median = ½ (base + base) Rhombi Angles all 90° Diagonals congruent All sides congruent Diagonals perpendicular Diagonals bisect opposite angles Squares Diagonals divide into 4 congruent triangles Isosceles Trapezoids Legs are congruent Base angle pairs congruent Diagonals are congruent 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