6.5 Trapezoids and 6.5 Trapezoids and kiteskites

Base anglesBase angles

Isosceles trapezoidsIsosceles trapezoids

MidsegmentsMidsegments

Trapezoid definition

A Trapezoid is a quadrilateral with only one pair of parallel sides.

Base

Base

LegLeg

1b

2b

h

AmgleBase

AmgleBase

AmgleBase

AmgleBase

Isosceles Trapezoids

Isosceles Trapezoids have congruent legs.

Base

Base

LegLeg

1b

2b

h

AmgleBase

AmgleBase

AmgleBase

AmgleBase

Theorem

In a Isosceles Trapezoid each pair of base angles are congruent.

Theorem

If a pair of base angles in a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

Theorem

In an Isosceles trapezoid the diagonals are congruent.

Definition of a Midsegment

Midsegment connect the midpoints of the legs.

Theorem

The Midsegment equal half the parallel sides sum.

Solve for NO =

The Midsegment equal half the parallel sides sum.

Definition of a Kite

A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent.

Theorem

Diagonals in a kite are perpendicular.

BDAC

Theorem

In a Kite, exactly one pair of opposite angles are congruent.

DB

Homework Homework

Page 359 – 362 Page 359 – 362

# 10 – 24 even, # 10 – 24 even,

25 – 27 , 25 – 27 ,

28 – 38 even28 – 38 even

Homework Homework

Page 359 – 362 Page 359 – 362

# 11 – 23 odd, # 11 – 23 odd,

31, 33 , 35, 37,31, 33 , 35, 37,

39, 48 -5239, 48 -52