5-m inute c heck 1 1) lmno is a rhombus. find x. 2) lmno is a rhombus. find y. 3) qrst is a square....

5-MINUTE CHECK 1

1) LMNO is a rhombus. Find x.

2) LMNO is a rhombus. Find y.

3) QRST is a square. Find n if mTQR = 8n + 8.

6-6 TRAPEZOIDS AND KITES

TRAPEZOID

Quadrilateral with one pair of parallel sides

Parallel sides are called the “bases”. Non-parallel sides are called the “legs”.

ISOSCELES TRAPEZOID

Trapezoid where the legs are congruent

Diagonals are congruent.

THEOREM

Base angles of an isosceles trapezoid are congruent.

What else can you tell me about angles x and y? They are supplements!

x x

y y

TOO: FIND THE MISSING ANGLES

1)

2)

70 70

110 110

35 35

145 145

THEOREM

The median of a trapezoid is parallel to the bases (Base + Base) divided by 2

b

b

m

2

b bm

EXAMPLE: EF IS THE MEDIAN OF TRAPEZOID ABCD

1) If AB = 25 and DC = 13, find EF.2) If AB = 29 and EF = 24, find DC.

TOO: If AB = 7y + 6, EF = 5y – 3, and DC = y – 5, find y and EF. (both answers are decimals!!)

A

E

D C

F

B

25 13

2EF

19

2924

2

DC

19

3.5 14.5

Kite

Is a Quadrilateral Diagonals are Perpendicular 2 consecutive sets of sides are congruent Longer diagonal bisects theAngles and the shorter diagonal.

EXAMPLE If MNPQ is a kite, find NP.

NR2 + MR2 = MN2 Pythagorean Theorem(6)2 + (8)2 = MN2

36 + 64 = MN2

100 = MN2

10 = MN

Since MN NP, NP = 10.

EXAMPLE

A. 28°

B. 36°

C. 42°

D. 55°

If BCDE is a kite, find mCDE.

HOMEWORK

Pg. 444 #8-11, 16-27, 41-44