1. Lesson 8-6
Trapezoids

2. 5-Minute Check on Lesson 8-5
Transparency 8-6
5-Minute Check on Lesson 8-5
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.
What property applies to a square, but not to a rhombus? L M N O P
(8y – 6)°
(3x + 12)°
(5x – 2)° 7 12
10.25 6 65 D Q R S T U
Standardized Test Practice: A
Opposite sides are congruent C
Diagonals bisect each other B
Opposite angles are congruent D
All angles are right angles
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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
Isosceles Trapezoids
Rectangles
Rhombi
Squares

6. Trapezoids Trapezoid Characteristics Bases Parallel
Legs are not Parallel
Leg angles are supplementary (mA + mC = 180, mB + mD = 180)
Median is parallel to bases Median = ½ (base + base) ½(AB + CD) A
base B
leg midpoint
leg midpoint
median C 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

7. Answer: Both trapezoids are isosceles.
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.
Example 6-2a

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

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

10. 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 m1 = 65° and 3 = 115°. Because 1  2 and 3  4, 2 = 65° and 4 = 115°
Example 6-4c

11. WXYZ is an isosceles trapezoid with medianb.
Answer:
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 bases Median = ½ (base + base)
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Rhombi
Isosceles Trapezoids
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Angles all 90°
Diagonals congruent
Squares
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Diagonals divide into 4 congruent triangles

13. Summary & Homework Summary: Homework:
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 ; 10, 13-16, 22-25