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Section 6-4/6-5 (1B): Special Parallelograms, Trapezoids and Kites
March 16, 2012
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
Warm-up
Warm-up
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
Warm-up
Questions on Homework?
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.
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
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
Properties of Quadrilaterals
Example 1
Find measures of the numbered angles for this rhombus
Example 2
Find measures of the numbered angles for these rhombuses
Example 3
Find missing angles and value of x in rectangle JOSH
Example 4
Find missing angles and value of y in rectangle CODY
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
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.
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)
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
Kite Applet
http://www.mathopenref.com/kite.html
Example 1: Find requested angle measures
Example 2: Find value of x in isosceles trapezoid SEAN
Example 3: Find perimeter of isosceles trapezoid CARL
Example 4: Find missing angle measures in KITE
Example 5: Find x and y
Example 6: Find x
Summary: Fill in everything you know
Isosceles Trapezoid Kite
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)