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Exploring the Properties of Kites: Consecutive Sides and Diagonal Relationships

This chapter delves into the unique properties of kites in geometry, focusing on shapes with consecutive sides that are equal. Students will investigate congruent sides, reflection properties, and the relationships formed by the diagonals of kites. Exercises include identifying congruent angles, calculating the area of kites, and determining if given shapes are kites based on slopes and lengths. Key properties discussed include perpendicular diagonals and the congruency of one pair of opposite angles, enhancing understanding of this fascinating geometric shape.

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Exploring the Properties of Kites: Consecutive Sides and Diagonal Relationships

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  1. 6.4 What If Consecutive Sides Are Equal? Pg. 15 Properties of Kites

  2. 6.4 – What If Consecutive Sides Are Equal?_ Properties of Kites In this chapter you have studied shapes that have opposite sides equal. Today you are going to investigate shapes that have consecutive sides equal.

  3. 6.20 – REFLECTION ON A SIDE Samuel decided to reflect the triangle in the picture, as shown. a. Based on this reflection, mark any sides that are congruent.

  4.  b. What shape did he make? What does this look like? Kite

  5. c. Complete the statements based on your reflection. • _______________________ sides are congruent • _______ pair of opposite angles are _________ consecutive one congruent

  6. d. Samuel continued studying this shape and decided to draw in the two diagonals. Help Samuel by drawing in the other diagonal. Label the point of intersection E. What relationship is formed where the two diagonals cross? Complete the statements below.

  7. perpendicular E

  8. e. List the properties of kites Consecutive sides are congruent Diagonals are perpendicular One pair of opposite angles congruent

  9. 6.21– ANGLES IN KITES WEST is a kite. Find the missing angles.

  10. 360 – 88 – 88 – 107 77°

  11. 360 – 29 – 95 2 = 118°

  12. 4 6.22 – AREA OF KITES Find the area of the kites. Don’t forget units.

  13. 4 ½(9)(4) ½(5)(4) 18 10 ½(5)(4) ½(9)(4) 10 18

  14. x2 + 242 = 252 x2 + 576 = 625 x = 7 84 7 52.5 52.5 84 7

  15. 6.23 – SHAPES ON THE GRID Determine if the shape is a kite by performing the following calculations:

  16. Slopes of: LM = MN = NO= OL=

  17. Lengths of: LM = MN = NO= OL=

  18. Kite

  19. Consecutive Sides Congruent • Diagonals are perpendicular • One pair of opposite angles congruent

  20. Add area of each triangle

  21. Parallelogram Trapezoid Isosceles Trapezoid Rectangle Rhombus Kite Square Triangle

  22. Triangle

  23. 3 sides

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