6-1 Classifying Quadrilaterals 1/23/17 Objective: To define and classify special types of quadrilaterals. PARALLELOGRAM: a quadrilateral with both pairs of opposite sides parallel RHOMBUS: a parallelogram with four congruent sides RECTANGLE: a parallelogram with four right angles SQUARE: a parallelogram with four congruent sides and four right angles

KITE: a quadrilateral with two pairs of adjacent sides congruent and no opposite sides are congruent TRAPEZOID: a quadrilateral with exactly one pair of parallel sides ISOSCELES TRAPEZOID: non parallel opposite sides are congruent Ex: Judging by appearances, classify DEFG in as many ways as possible. DEFG is a quadrilateral, parallelogram, and a rectangle D E F G

QUADRILATERAL PARALLELOGRAM WXYZ is a RHOMBUS Judging by appearance, classify WXYZ in as many ways as possible. What is the best description? QUADRILATERAL PARALLELOGRAM KITE RHOMBUS TRAPEZOID RECTANGLE ISOSCELES TRAPEZOID W X Y Z 2 Pair // Sides 0 Pair // Sides 1 Pair // Sides SQUARE

Ex: Determine the precise name for quadrilateral LMNP STEP 1: Find slope of each side Slope of LM 3 – 2 = 1 3 – 1 2 Slope of NP 2 – 1 = 1 5 – 3 2 Slope of MN 3 – 2 = -1 N(5,2) 3 – 5 2 Slope of LP 2 – 1 = -1 1 – 3 2 2 pairs of parallel sides, so LMNP is a parallelogram. But could it be more?.... M (3, 3) L (1, 2) P (3, 1)

Distances are all 26, so it is a SQUARE. STEP 2: Use distance formula to see if any pairs of sides are congruent LM = (3 – 1)2 + (3 – 2)2 = 5 NP = (5 – 3)2 + (2 – 1)2 = 5 MN = (3 – 5)2 + (3 – 2)2 = 5 LP = (1 – 3)2 + (2 – 1)2 = 5 All sides are congruent so LMNP is a Rhombus Determine the most precise name for quadrilateral ABCD with vertices A (-3,3), B (2,4), C (3, -1), and D (-2,-2) 2 Pair of parallel sides (m = 1/5 and m = -5) so it’s a parallelogram. Since slopes are opposite reciprocals, those are right angles, and it is a rectangle. Distances are all 26, so it is a SQUARE.

Ex: Find the values of the variables for the kite Ex: Find the values of the variables for the kite. KB = JB Definition of Kite 3x – 5 = 2x + 4 Substitution x – 5 = 4 x = 9 KT = x + 6 = 9 + 6 = 15 (Substitution) KT = JT Definition of Kite 15 = 2y + 5 Substitution 10 = 2y y = 5 T 2y + 5 x + 6 J K 2x + 4 3x – 5 B

Find the values of the variables for the rhombus Find the values of the variables for the rhombus. Then find the lengths of the sides. 3b + 2 = 4b – 2 4 = b 3b + 2 14 14 3a + 8 5a + 4 = 3a + 8 5a + 4 14 14 2a = 4 4b – 2 a = 2

Judging by appearance, classify the quadrilaterals in as many ways as possible. What are their most precise names? 2) Find the values of the variables in the rhombus Parallelogram RECTANGLE KITE a + 2a = 180 (S.S.I.A.!) A x B a° 2a° a = 60 3x – 12 x = 3x – 12 8 – y x = 6 C 6 = 8 – y D y = 2

Assignment: Page 290 #1 – 12, 19 – 26