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Section 5.4 Four-Sided Polygons By: Laura Moeller Kristie Furiosi

Section 5.4 Four-Sided Polygons By: Laura Moeller Kristie Furiosi. WHAT IS A POLYGON?. A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. The following are examples of polygons:. WHAT IS NOT A POLYGON?.

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Section 5.4 Four-Sided Polygons By: Laura Moeller Kristie Furiosi

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  1. Section 5.4 Four-Sided Polygons By: Laura Moeller Kristie Furiosi

  2. WHAT IS A POLYGON? • A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. • The following are examples of polygons:

  3. WHAT IS NOT A POLYGON? • The figure below is not a polygon since it is not a closed figure: • The figure below is not a polygon since it is not made of line segments:

  4. Naming Polygons • Polygons are named starting at one vertex, then continuing clockwise or counter-clockwise. • This polygon can be named LKBFJM, or LMJFBK starting at point L. (Polygon Laura Kristie Beatrice Furiosi Jane Moeller) L K B F J M

  5. Diagonals of Polygons • Diagonals are the segments that connect two nonconsecutive vertices of the polygon. • LV and EO are diagonals of rectangle LOVE. L O E V

  6. QUADTILATERALS QUADRILATERALS: four-sided polygons The following are examples of quadrilaterals:

  7. TYPES OF QUADRILATERALS • PARALLELOGRAM- a quadrilateral in which both pairs of opposite sides are parallel or congruent. K F K F L M L M

  8. TYPES OF QUADRILATERALS • RECTANGLE- a parallelogram in which at least one angle is a right angle Figure HANK is a parallelogram H A K N <N is a right angle, therefore, HANK is a rectangle

  9. TYPES OF QUADRILATERALS • RHOMBUS- A parallelogram in which at least two consecutive sides are congruent.

  10. TYPES OF QUADRILATERALS • KITE- a quadrilateral in which two disjoint pairs of consecutive sides are congruent.

  11. TYPES OF QUADRILATERALS • SQUARES- a parallelogram that is both a rectangle and a rhombus.

  12. TYPES OF QUADRILATERALS • TRAPEZOID- a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases of the trapezoid. B A D C

  13. TYPES OF QUADRILATERALS • ISOSCELES TRAPEZOID- a trapezoid in which the nonparallel sides (legs) are congruent.

  14. Sample Problem 1 K Given: KFLM is a kite. KF = x + 7 FL = x + 8 LM = 3x – 7 MK = 4x – y • Solve for x and y. • What is the perimeter of the kite? M F L

  15. Answer to Sample Problem 1 x + 8 = 3x – 7 4x – y = x + 7 -2x = -7 – 8 4(7.5) – y = 7.5 + 7 -2x = -15 30 – y = 14.5 x = 7.5 -y = 14.5 – 30 -y = -15.5 y=15.5 • x = 7.5, y = 15.5 • Perimeter of KFLM = 60

  16. Sample Problem 2 Find the area of a square if the perimeter is 70. A B D C

  17. Answer to Sample Problem 2 70 4 = 17.5 17.5 x 17.5 = 306.25 The area of square ABCD is 306.25 A B C D

  18. Practice Problems True of False? A rectangle has four congruent sides… A parallelogram has one pair of opposite sides parallel… The non-parallel sides of a trapezoid are the bases… A quadrilateral has four sides… A rectangle has at least one right angle…

  19. Answers to Practice Problems True or False? False- only the opposite sides of a rectangle are congruent. False- A parallelogram has two pairs of opposite sides parallel. False- The non-parallel sides of a trapezoid are the legs. True True

  20. More Practice Problems Examine the statements below. If the statement is always true, write A; if sometimes true, write S; if never true, write N. • A rectangle is a polygon. • A trapezoid has 3 bases. • A kite is a parallelogram. • A square is a rhombus.

  21. Answers to Practice Problems • Always • Never – a trapezoid only has 2 bases • Sometimes – a rhombus is not only a kite, but a parallelogram • Always

  22. POLYGON VIDEO

  23. WARNING RANDOM POLYGON VIDEOmay cause extreme headaches and annoyance

  24. Works Cited "2D Geometric shapes." Math Worksheets, Tables, Charts and more from HelpingWithMath.com. Web. 17 Jan. 2010. <http://www.helpingwithmath.com/by_subject/geometry/geo_shapes.htm>. "Figures and Polygons." Web. 17 Jan. 2010. <http://www.mathleague.com/help/geometry/polygons.htm>. Milauskas, George, and Robert Whipple. Geometry for Enjoyment & Challenge. Boston: Houghton Mifflin Company, 1991. Print. "Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram." Math is Fun - Maths Resources. Web. 17 Jan. 2010. <http://www.mathsisfun.com/quadrilaterals.html>.

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