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Page 1: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Trapezoids and Kites

1/16/13Mrs. B

Page 2: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Objectives:

Use properties of trapezoids.Use properties of kites.

Page 3: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Using properties of trapezoids

A trapezoid is a quadrilateral with exactly one pair of parallel sides called bases.

A trapezoid has two pairs of base angles. Ex. D and C

And A and B. The nonparallel sides

are the legs of the trapezoid.

base

base

legleg

A B

D C

Page 4: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Using properties of trapezoids

If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

Page 5: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Isosceles Trapezoid

If a trapezoid is isosceles, then each pair of base angles is congruent.A ≅ B, C ≅ D

A B

D C

Page 6: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Isosceles Trapezoid

If a trapezoid is isosceles, then adjacent angles (not bases) are supplementary.<A + <D = 180<B + <C = 80

A B

D C

Page 7: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Ex. 1: Using properties of Isosceles Trapezoids

Given, angle X is 50Find <R, < P and <Q,

m PS = 2.16 cm

m RQ = 2.16 cm

S R

P Q

50°

Page 8: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Isosceles Trapezoid

A trapezoid is isosceles if and only if its diagonals are congruent.

ABCD is isosceles if and only if AC BD.≅

A B

D C

Page 9: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Midsegment of a trapezoid

The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

midsegment

B C

DA

Page 10: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Theorem 6.17: Midsegment of a trapezoid

The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases.

MN║AD, MN║BC MN = ½ (AD + BC)

NM

A D

CB

Page 11: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Ex. 3: Finding Midsegment lengths of trapezoids

LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?

Page 12: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites
Page 13: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Ex. 3: Finding Midsegment lengths of trapezoids

Use the midsegment theorem for trapezoids.

DG = ½(EF + CH)=½ (8 + 20) = 14” C

D

E

D

G

F

Page 14: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Using properties of kites

A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Page 15: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Kite theorems

Theorem 6.18 If a quadrilateral is a

kite, then its diagonals are perpendicular.

AC BD

B

CA

D

Page 16: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Kite theorems

Theorem 6.19 If a quadrilateral is a

kite, then exactly one pair of opposite angles is congruent.

A ≅ C B not =D

B

CA

D

Page 17: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Ex. 4: Using the diagonals of a kite

WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths.

WX = XY =

12

1220

12

U

X

Z

W Y

Page 18: Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites

Ex. 5: Angles of a kite

Find mG and mJ

in the diagram.

J

G

H K132° 60°


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