UNIT 7 - DAY 46-5 Trapezoids and Kites

Warm Up

Which statement is true?a. All quadrilaterals are rectanglesb. All quadrilaterals are parallelogramsc. All rectangles are parallelogramsd. All rectangles are squares

In the rhombus below, m∠1=30x,

m∠2=z+y, and m∠3=5z. Find the value of each variable

Agenda

1. Warm Up2. Homework Check 3. 6-5: Trapezoids and Kites4. Class Work 5. Homework

Homework Check 1. 12 2. 40 3. 41 4. 18

5. 526. 1=55, 2=55, 3=35, 4=35, 5=55, 6=55, 7=35,

8=70, 9=110, 10=70 PQ=10, QO=10, MO=207. 1=58, 2=32, 3=32, 4=58, 5=58, 6=32, 7=32,

8=90, 9=90, 10=90 ST = 23.58. 1=25, 2=25, 3=65, 4=65, 5=25, 6=25, 7=65,

8=65, 9=90, 10=90, 11=90, 12=909. 1-7=45, 9-12=9010. rfg=90, 90, 90, for=45, 45, 45, fsg=90, 90,

gfo=45, 45, ogf=90, 90

6-5 Trapezoids and Kites

TrapezoidDefinition: a quadrilateral with 1 pair of parallel sides The parallel sides are called bases The nonparallel sides are called legs Base Angles: ∠1 and ∠2, ∠4 and ∠3

Property: Consecutive angles along the legs are supplementary (sum to 180)

m∠1 + m∠4 = 180m∠2 + m∠3 = 180

Isosceles Trapezoid

Definition: A trapezoid with congruent legs

Properties: All Trapezoid properties Diagonals are (TA RP) Two pairs of base angles that are congruent

m∠4 m∠3

m∠1 m∠2

Ex 1

a) If m∠F = 130

Find: m∠R=_____ m∠G=_____m∠O=____

b)

If m∠R=2x-10 and m∠O =3x

Find m∠G.

c)

If FO = 2x+3 and GR=3x-1.Find x

Median of a Trapezoid

Definition: Segment that connects midpoints of legs.

2(median) = sum of bases2(TP) = AB + DC

Ex 2:

OL = 28, RM = 20. Find CA

Ex 3:

CA= 8x, RM= 2x + 6, OL = 4x + 6. Find OL

Kite:

Definition: A quadrilateral with 2 pairs of adjacent sides congruent

Properties: Diagonals are One pair of congruent opposite ∠’s Diagonals bisect top and bottom angles

Ex 4:

m<1 = 48

Find m< 2 = _______m< 3 = _______m< 4 = _______

Homework

Complete Worksheet