1 / 22

Chapter 8

Chapter 8. Quadrilaterals. What is a quadrilateral?. A polygon that has four sides. Examples. Classification of Quadrilaterals. Two pairs of parallel sides (Parallelogram) One pair of parallel sides (Trapezoid) No sides parallel (Kite). A quadrilateral with 2 pairs of parallel sides.

fisk
Download Presentation

Chapter 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 Quadrilaterals

  2. What is a quadrilateral? • A polygon that has four sides. Examples

  3. Classification of Quadrilaterals • Two pairs of parallel sides (Parallelogram) • One pair of parallel sides (Trapezoid) • No sides parallel(Kite)

  4. A quadrilateral with 2 pairs of parallel sides What is a parallelogram Example A B C D

  5. What is a rectangle? • A Quadrilateral with 4 right angles Example A B C D

  6. What is a rhombus A Quadrilateral with 4 congruent sides A D B C

  7. What is a Square A quadrilateral with 4 right angles and 4 congruent sides Example A B D C

  8. Types of parallelograms • Rectangles • Rhombus • Square

  9. Both pairs of opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary AB || DC & AD || BC AB = DC & AD = BC <A = <C & <B = <D <A + <B = 180 <B + <C = 180 <C + <D = 180 <D + <A = 180 Properties of a parallelogram

  10. 5. Diagonals bisect each other AE = EC & DE = EB Properties of parallelogram cont.

  11. 5 properties of a ||ogram + 6. 4 right angles 7. Diagonals are congruent <A, <B, <C, & <D are right angles AC = DB Properties of a rectangle

  12. 5 properties of a ||ogram + 6. 4 sides are congruent 7. Diagonals are perpendicular 8. Diagonals bisect opposite angles AB = BC = CD = DA <AEB is a right angle <ABE = <EBC Properties of a rhombus

  13. Properties of a square • All properties of a ||ogram • All properties of a rectangle • All properties of a rhombus

  14. A Quadrilateral is a parallelogram if any one of the following is true. • Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • Diagonals bisect each other. • A pair of opposite sides is both parallel and congruent.

  15. Trapezoid • A quadrilateral with one pair of sides parallel

  16. Bases Legs Base angles Sides that are parallel Nonparallel sides (congruent sides) A pair of angles on the same side with a base Parts of a trapezoid base leg leg Base angle base Base angle

  17. Special Trapezoid • Isosceles Trapezoid – trapezoid that has congruent legs

  18. Properties of Isosceles Trapezoid • Legs are congruent • Both pairs of base angles are congruent • The diagonals are congruent

  19. What is a median ? • Segment that joins the midpoints of the legs • Parallel to the bases

  20. Finding the median • Median = ½ (base1 + base2)

  21. Example • Given trapezoid GHIJ with median KL, find the value of x. KL = ½ (GH + JI) 10 = ½ ( 3x – 1 + 7x +1) 10 = ½ ( 10x ) 10 = 5x 2 = x G 3x – 1 H 10 L K J 7x + 1 I

  22. Example 2 • Given trapezoid WXYZ with median MN, find XY, if MN = 10 and WZ = 14. MN = ½(XY + WZ) 10 = ½ (XY + 14) 20 = XY + 14 6 = XY Z W N M X Y

More Related