Download Sec6-5 Lesson Plan - epawelka-math

Elizabeth Pawelka
Trapezoids and Kites
3/15/12
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Geometry
Lesson Plans
Section 6-5: Trapezoids and Kites
3/16/12 (2B; 4B on 3/19)
Warm-up (15 mins)
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Practice Book, 6-4, p. 70: # 1-13
Copy and complete this table (2B). Check which properties each quadrilateral has.
Property
Parallelogram
Rhombus
x
Rectangle
Square
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
All sides are ≅
Opposite sides are ≅
Opposite sides are ||
Opposite angles are ≅
All angles are right ∠’s
Diagonals bisect each other
Diagonals are ≅
Diagonals are ┴
Each diagonal bisects
opposite angles
x
x
x
x
x
x
Elizabeth Pawelka
Trapezoids and Kites
3/15/12
Complete this table (4B)
Go over warm-up (5 mins)
Homework Review (10 mins) – ask for any questions on homework.
p. 315 – 317. #1-21, 48, 50, 54, 57
Statement of Objectives (5 mins)
The student will be able to use properties of trapezoids and kites.
Teacher Input (55 mins)
Properties of Quadrilaterals
Trapezoid
 Parallel sides are called bases.
 Non-parallel sides are called legs.
 Angles that share a leg are supplementary. (Due to Same Side Interior angles)
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Elizabeth Pawelka
Trapezoids and Kites
3/15/12
p.3
Isosceles Trapezoid
 Properties of a trapezoid
 Legs are congruent (def)
 Base angles are congruent (Thm 6-15) Note that it actually forms an isosceles triangle and that’s
why the base angles are congruent
 Diagonals are congruent (Thm 6-16)
Kite
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Diagonals are perpendicular (Thm 6-17)
A diagonal bisects the angles formed by the congruent sides (or the vertex angles of the isosceles
triangles formed)
Angles formed by non-congruent sides are congruent
Elizabeth Pawelka
Trapezoids and Kites
3/15/12
p.4
Show applet at http://www.mathopenref.com/kite.html to show that the opposite angles (red above) are
always congruent and the diagonal is always 90 degrees.
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Create a kite with two 90 degree angles to show that it can happen in a kite (and not be a
rectangle! – on test!)
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Point out that points A and C are always the same distance from B and D (endpoints of a
segment that AC is perpendicular to … what does that make AC? A perpendicular bisector! So,
that means that BD is bisected. But AC is not bisected.
Example 1: Find requested angle measures
m∠A = __24___
m∠B = __156___
m∠C = __156___
Example 2: Find value of x in isosceles trapezoid SEAN
5x - 2 = 2x + 16
3x = 18
x=6
SA = 5x - 2
EN = 2x + 16
Elizabeth Pawelka
Trapezoids and Kites
3/15/12
p.5
Example 3: Find perimeter of isosceles trapezoid CARL
x + 5 = 3x -2
7=x
Perimeter = 12 + 12 + 6 + 17 = 47
Example 4: Find missing angle measures in KITE
1 = 72 (opposite angles congruent)
2 = 90 (perpendicular)
3 = 18 (90 – 72)
4 = 27 (90 – 63)
Elizabeth Pawelka
Trapezoids and Kites
3/15/12
Example 5: Find x and y
3x + 3 = x + 13
2x = 10
x=5
x+6=y–5
5+6=y–5
16 = y
Example 6: Find x
4x + (2x + 6) = 90
6x = 84
x = 14
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Elizabeth Pawelka
Trapezoids and Kites
3/15/12
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Summary: Draw everything you know about Trapezoids and Kites – pick 2 students to come up and fill
in the drawings:
Isosceles Trapezoid:
Kite:
Closure (5 mins)
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Today you learned to use properties of trapezoids and kits.
On Monday you’ll learn about figures on the coordinate plane.
!!!! Reminder: Quiz on Monday on Sections 6-1 through 6-4 !!!!
Homework (Both)
p. 322 – 324: # 1-16, 18, 20-25, 27-29