6.4

What If Consecutive Sides Are Equal?Pg. 16

Properties of Kites

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.

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

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

Kite

c. Complete the statements based on your reflection. • _______________________ sides are congruent 

• _______ pair of opposite angles are _________

consecutive

one congruent

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.

BD is____________ to AC

AE ____________

perpendicular

E

EC

e. List the properties of kites

Consecutive sides are congruent

Diagonals are perpendicularOne pair of opposite angles congruent

6.21– ANGLES IN KITESWEST is a kite. Find the missing angles.

88

77

360 – 88 – 88 – 107

77°

360 – 29 – 95 2 = 118°

6.22 – AREA OF KITESFind the area of the kites. Don’t forget units.

4

4½(9)(4)

18

½(9)(4) 18

½(5)(4) 10

½(5)(4) 10

A un256

x2 + 242 = 252

x2 + 576 = 625x = 7

7

7

84

84

52.5

52.5

A un2273

6.23 – SHAPES ON THE GRIDDetermine if the shape is a kite by performing the following calculations:

Slopes of: LM = MN =

NO = OL =

0 6

0 6

Lengths of: LM = MN =

NO = OL =

62 12 x2

36 1 x2

3 37

62 12 x2

36 1 x2

3 37 parallelogram

Parallelogram

Rectangle

Rhombus

Square

Trapezoid

IsoscelesTrapezoid

Kite

Triangle

Kite

• Consecutive Sides Congruent

• Diagonals are perpendicular

• One pair of opposite angles congruent

Add area of each triangle