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Skip a page for your stampsheet! Warm up #1 11/6/17 Monday
• Segment above had been bisected by point M. Solve for x with the given informaCon.
A B
AM = 3x −13MB = x +1
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15.2-‐15.3 Trapezoids and Parallelograms
EQ: How do you develop and prove properCes of Trapezoids and parallelograms?
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• The parallel sides are called the bases. • The nonparallel sides are called the legs.
leg leg
base
A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides.
base A
B C
D
BC || AD
AB ||CD
m∠A+m∠B =180°m∠C +m∠D =180°
Same-‐Side Interior Angles
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Trapezoid Example 1 Find the measurement of the angle indicated.
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Isosceles Trapezoid
• DefiniCon: A trapezoid with congruent legs
• Each pair of base angles is congruent
• Diagonals are congruent
AB ≅CD
leg leg
base
base A
B C
D
∠A ≅∠D ∠B ≅∠C
AC ≅ DB
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Isosceles Trapezoid Example
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Median of a Trapezoid
• A segment joining the midpoints of the legs • Length of the median is equal to ½ Cmes the sum of the bases
lmedian =12(b1 + b2 ) 3
5
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Median of the Trapezoid Example
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Area of a Trapezoid
• Area = ½h (b1 + b2) • H = height of the trapezoid • b1 = one of the bases • b2 = the other base 40 units
70 units
50units
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Parallelogram A Parallelogram is a quadrilateral with both pairs of opposite sides parallel and congruent.
A
B C
D
AB ||CDBC || AD
AB ≅CD
BC ≅ AD
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Angles of a Parallelogram
A
B C
D
∠A ≅∠C ∠B ≅∠D
m∠A+m∠B =180o
m∠C +m∠D =180o
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Diagonals of a Parallelogram
A
B C
D
The diagonals of a parallelogram bisect each other.
M
BM ≅ DM AM ≅CM
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You Try Pg. 215 #11 &12
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What’s due NEXT MONDAY?
• Springboard Pg. 221 #2-‐7
• UNIT 2 TEST Wednesday!