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Understanding Quadrilaterals: Types, Properties, and Examples

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This chapter provides a comprehensive overview of quadrilaterals, including their definition and classifications. It discusses the properties of various types of quadrilaterals such as parallelograms, rectangles, rhombuses, and squares. Additionally, the chapter covers trapezoids, including isosceles trapezoids, and explains important concepts such as the median of a trapezoid. Examples and visual aids are provided to illustrate the properties and characteristics of each type. This foundational knowledge is essential for understanding more complex geometric concepts.

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Understanding Quadrilaterals: Types, Properties, and Examples

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  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

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