Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 1 LESSON 6.1 CLASSIFYING QUADRILATERALS OBJECTIVE: To define and classify special types of quadrilaterals

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 2 A ___________ is a four-sided polygon. A ____ is a quadrilateral with two pairs of adjacent sides  and no opposite sides . NO PAIRS OF PARALLEL SIDES quadrilateral kite

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 3 A __________ is a quadrilateral with exactly 1 pair of parallel sides. An __________________ is a trapezoid whose nonparallel sides are . 1 PAIR OF PARALLEL SIDES trapezoid isosceles trapezoid

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 4 A _____________ is a quadrilateral with both pairs of opposite sides parallel. A _________ is an equilateral parallelogram. A _________ is an equiangular parallelogram. A _______ is an equilateral and equiangular parallelogram. 2 PAIRS OF PARALLEL SIDES parallelogram rhombus rectangle square

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 5 Special Quadrilaterals kites True or false: A square is a rectangle and a rhombus. Explain. Page Modified on 1/28/08

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 6 Properties of Parallelograms: Angles Use Same-Side Interior Angle Theorem to find the missing angles in the parallelogram below: supplementary 120 a c b The consecutive angles in a are _____________. The opposite angles in a are _____________. congruent

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 7 Check for Understanding: Summary Properties of Parallelograms Opposite sides are _________________. (DEF.) Opposite sides are _________________. Opposite angles are ________________. Consecutive angles are _____________>

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 8 Check for Understanding: Properties of Special Quadrilaterals ParallelogramRhombusRectangleSquare Equilateral Equiangular Opp. Sides // Opp. Sides = Opp. Angles =

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 9 EXAMPLE #1 In parallelogram RSTU, m  R = 2x – 10 and m  S = 3x Find x. U T S R 2x – 10 3x x – x + 50 = 180 5x + 40 = 180 5x = 140 x = 28 m  R + m  S = 180 RU || ST Def of Parallelogram Substitution Simplify Subt prop of = Div prop of = SSI Alert! Consecutive angles of a parallelogram are supplementary.

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 10 EXAMPLE #2 Find the values of the variables in the rhombus. Then find the lengths of the sides. L N T S 3b + 2 4b – 2 5a + 4 3a + 8 Find a. 5a + 4 = 3a + 8 2a = 4 a = 2 Find b. 4b – 2 = 3b + 2 b = 4 LN =3b + 2 =3(4) + 2 =14 ST =4b – 2 =4(4) – 2 =14 LS =5a + 4 =5(2) + 4 =14 NT =3a + 8 =3(2) + 8 =14 Alert! Opposite sides of a parallelogram are congruent.

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 11 Classifying Quadrilaterals During this lesson, you will classify quadrilaterals algebraically by using Distance Formula and Slope Formula.

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 12 Algebra Review Two lines which have the same slope are _____________ to each other. Two lines whose slopes are negative (opposite) reciprocals are ___________________ to each other. Given two points (x 1, y 1 ) and (x 2, y 2 ), write: Slope Formula: ____________________ Distance Formula:__________________ parallel perpendicular

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 13 EXAMPLE #3 Determine the most precise name for the quadrilateral with vertices A(-3,3), B(2,4), C(3,-1) and D(-2,-2). 1. Graph quadrilateral ABCD. A B C D

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 14 EXAMPLE #3 Determine the most precise name for the quadrilateral with vertices A(-3,3), B(2,4), C(3,-1) and D(-2,-2). Explain your response. 2.Find the slope of each side. Slope AB = Slope BC = Slope CD = Slope DA = 4 – 3 2 – (-3) -1 – 4 3 – 2 -2 – (-1) -2 – 3 3 – (-2) -3 – (-2) = -5 5 = -5 = = = = = AB || CD and BC || DA b/c same slope AB  DA, AB  BC, CD  DA and CD  BC b/c opposite reciprocal slopes

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 15 EXAMPLE #3 Determine the most precise name for the quadrilateral with vertices A(-3,3), B(2,4), C(3,-1) and D(-2,-2). 2.Find the length of each side. AB = BC = CD = DA = = = = = = = = = All sides have the same length. The most precise name for the quad is a square.

Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08 16 ASSIGNMENT Pg 290 #1-13 (graph paper needed for #13), even, 37-42