Trapezoids
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This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.
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Trapezoids
- 2. a quadrilateral with exactly one pair of parallel sides. Leg Leg Base Base A B C D Trapezoid
- 3. A B C D Leg Angles are Supplementary Property of a Trapezoid A + C = 180 B + D = 180
- 4. Isosceles Trapezoid Definition - A trapezoid with congruent legs.
- 5. Properties of Isosceles Trapezoid 1) Base Angles Are Congruent 2) Diagonals Are Congruent 3) Leg Angles are Supplementary A B C D
- 6. Example Find m P, m Q and mR. 50 S R P Q
- 7. Given: m A= 78属, Find C.
- 8. Given: AC = 17.5, AE = 9.6, find BE and BD. E
- 9. Given: MNOP is an isosceles trapezoid with diagonal PN. m O= 72属, m NPO = 47属, Find m M and m MNP.
- 10. Given: JACK is an isosceles trapezoid with diagonal PN. m J= (5x+13)属, m K = (3x-1)属, Find m J and m K.
- 11. Midsegment 2 21 bb Midsegment = Line that parallel to both bases. Connects the midpoints of the legs. Its length is equal to half of the sum of the length of the bases
- 12. Given the figure at the right. ABCD is an Isosceles trapezoid with the midsegment EF. GH is a midsegment of I.T ABFE. If m D= 74属, AB=34 and CD=26, find EF, GH, m C, m AEF, m BFE, m AGH and mBHG.
- 13. Using Properties of Trapezoids Find the area of this trapezoid.
- 14. Using Properties of Trapezoids Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.