section 6-4/6-5 (1b): special parallelograms, trapezoids and kites march 16, 2012
TRANSCRIPT
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Section 6-4/6-5 (1B): Special Parallelograms, Trapezoids and Kites
March 16, 2012
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Warm-up: (15 mins)
Practice Book (6-2), p. 66: #2 – 8
(even), 9 -12, 14 – 20 (even) Practice Book (6-3), p. 68: # 1 – 6
(even), 13 - 20
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Warm-up
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Warm-up
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Warm-up
Practice Book (6-2), p. 66: #2 – 8
(even), 9 -12, 14 – 20 (even) Practice Book (6-3), p. 68: # 1 – 6,
13 - 20
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Warm-up
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Questions on Homework?
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Sections 6-4 and 6-5: Special Parallelograms, Trapezoids and Kites
Objectives: You will learn to use properties of diagonals of rhombuses
and rectangles, and properties of trapezoids and kites.
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Properties of Quadrilaterals
Parallelogram Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other
Rhombus: Parallelogram with 4 congruent sides Properties of Parallelogram All sides are congruent Each diagonal bisects opposite angles Diagonals are perpendicular
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Properties of Quadrilaterals
Rectangle: Parallelogram with 4 right angles Properties of Parallelogram All angles are right angles Diagonals are congruent
Square: Parallelogram with 4 congruent sides (rhombus) and 4 right angles (rectangle)
Properties of Parallelogram Properties of Rhombus Properties of Rectangle
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Properties of Quadrilaterals
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Example 1
Find measures of the numbered angles for this rhombus
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Example 2
Find measures of the numbered angles for these rhombuses
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Example 3
Find missing angles and value of x in rectangle JOSH
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Example 4
Find missing angles and value of y in rectangle CODY
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Copy and Fill in TableProperty Parallelogram Rhombus Rectangle Square
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
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Section 6-5: Trapezoids and Kites
Trapezoid Parallel sides are called bases. Non-parallel sides are called legs. Angles that share a leg are supplementary.
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Section 6-5: Trapezoids and Kites
Isosceles Trapezoid Properties of a trapezoid Legs are congruent (def) Base angles are congruent (Thm 6-15) Diagonals are congruent (Thm 6-16)
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Section 6-5: Trapezoids and Kites
Kite Diagonals are
perpendicular A diagonal bisects the
angles formed by the congruent sides
Angles formed by non-congruent sides are congruent
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Kite Applet
http://www.mathopenref.com/kite.html
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Example 1: Find requested angle measures
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Example 2: Find value of x in isosceles trapezoid SEAN
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Example 3: Find perimeter of isosceles trapezoid CARL
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Example 4: Find missing angle measures in KITE
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Example 5: Find x and y
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Example 6: Find x
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Summary: Fill in everything you know
Isosceles Trapezoid Kite
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Wrap-up Today you learned to use properties of diagonals
of rhombuses and rectangles and about trapezoids and kites.
Monday you’ll learn about figures on the coordinate plane.
!!!! Reminder: Quiz on Monday !!!!
Homework p. 315 – 317, # 1-21 (odd), 48-50, 57 p. 322 – 324, # 1-15 (odd), 18, 21-29 (odd)