1. 6-5 Trapezoids and Kites 2/15/17
Objective: To verify and use properties of trapezoids and kites. BASE ANGLES: two angles that share a base of a trapezoid THEOREM 6-15 The two pairs of base angles of an isosceles trapezoid are congruent. W
base X
W & X are a pair of base angles.
Base Angles
leg
leg
Y & Z are another pair of base angles. Y Z
base

2. Ex: ABCD is an isosceles trapezoid and m B = 102
Ex: ABCD is an isosceles trapezoid and m B = 102. Find m A, m C, and m D. C = 102°(base angles =) A = 78°(supp to B) D = 78°(base angles =) B C
102° A D

3. In the isosceles trapezoid, m S = 70. Find m P, m Q, and m R.
Angle P = 110
Angle Q = 110
70°
Angle R = 70 R S
Theorem 6-16
The diagonals of an isosceles trapezoid are congruent.

4. THEOREM 6-17 The diagonals of a kite are perpendicular
THEOREM 6-17 The diagonals of a kite are perpendicular. Ex: Find m 1, m 2, and m 3 in the kite.
Angle 1 = 90 (diagonals of kite are perpendicular) B
Angle 2 = 58 (180 – 32 – 90)
32° 3
Angle 3 = 32 (Δ ABD = Δ BCD; CPCTC ) 1 2 A C D

5. Find m 1, m 2, and m 3 in the kite.
Angle 1 = 90 (diagonals of kite are perpendicular)
Angle 2 = 46 (Δ’s are congruent; CPCTC )
Angle 3 = 44 (180 – 90 – 46)
46° 1 2 3

6. ABCD is an isosceles trapezoid
If m A = 45, find m B, m C, and m D.
If AC = 3x – 16 and BD = 10x – 86, Find x
GHIJ is a kite
1) Find m ) Find m 2
3) Find m ) Find m 4
45°
135°
135°
x = 10 H 4
50° G I 3 1 2
19° J
90°
19°
71°
40°

7. Assignment:
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