6.5Trapezoids & Kites

Trapezoid

• Is a quadrilateral with exactly 1 pair of parallel sides

Trapezoid

A B

C D

leg

leg

BASE

BASE

If the legs are congruent then the trapezoid is an isosceles trapezoid.

Theorem 6.14•If a trapezoid is isosceles, then each pair of base angles is congruent.

Theorem 6.15•If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Theorem 6.16•A trapezoid is isosceles if and only if its diagonals are congruent.

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

THM 6.17• The midsegment of a

trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases

21 basebase2

1midsegment

EX 1 Find the length of MN.

13

P Q

M N

S R

10

16

EX 2 Find the value of x.

19 15 17 x

A Kite•A quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.

Theorem 6.18•If a quadrilateral is a kite, then its diagonals are perpendicular.

Theorem 6.19•If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

Ex 3 Find the measure of the sides. Round to the nearest tenth.

LM = 3.6LO = 3.6ON= 5MN = 5

L

M

N

O

2

3 3

4

Ex 4 Find the mL.

110

40

100

L

M

N

O

Ex 5 Find the mL.

3555

135

x

L

M

N

O

Add Trapezoid and Kite to your foldable.

Goal: Identify midsegments and use properties of midsegments of a triangle

Midsegment – a segment that connects the midpoints of two

sides of a triangle.

Midsegment Theorem

A

B

C

X Y

AC || XY

XY = ½ AC

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

Ex 1: UW and VW are midsegments of RST. Find UW and RT.

R

S

T

V

W

U

128

UW = 6

RT = 16

Ex 2: X, Y, and Z are the midpoints of UVW. Complete each statement.

U

X

V WZ

Y

a. If VW = 6a, then XY = ___

b. mWZY = 2b + 1, then mWVU = ______.

c. XZ _______.

d. If YZ = c, then UV = ____