Unit 7 - Day 4 6-5 Trapezoids and Kites

Warm Up Which statement is true? In the rhombus below, m∠1=30x, All quadrilaterals are rectangles All quadrilaterals are parallelograms All rectangles are parallelograms 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 Warm Up Homework Check 6-5: Trapezoids and Kites Class Work

Homework Check 12 2. 40 3. 41 4. 18 5. 52 6. 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=20 7. 1=58, 2=32, 3=32, 4=58, 5=58, 6=32, 7=32, 8=90, 9=90, 10=90 ST = 23.5 8. 1=25, 2=25, 3=65, 4=65, 5=25, 6=25, 7=65, 8=65, 9=90, 10=90, 11=90, 12=90 9. 1-7=45, 9-12=90 10. rfg=90, 90, 90, for=45, 45, 45, fsg=90, 90, gfo=45, 45, ogf=90, 90

6-5 Trapezoids and Kites Trapezoid Definition: 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 = 180 m∠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 bases 2(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