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)