Special Quadrilaterals Unit 6: Lesson #2 Special Quadrilaterals Warm-up: Quadrilateral Vocab (on the front table)

Quadrilateral Vocab ۞ A quadrilateral is a _4_ sided polygon. Name Definition Picture PARALLELOGRAM Opposite sides are // RHOMBUS Parallelogram (TWO pairs of // sides) All sides are congruent

Quadrilateral Vocab Name Definition Picture RECTANGLE Parallelogram (TWO pairs of // sides) All angles are exactly 90. SQUARE Parallelogram (TWO pairs of // sides) All sides are congruent . All angles are exactly 90.

Quadrilateral Vocab KITE 2 pairs of congruent consecutive sides. TRAPEZOID Exactly one pair of parallel sides. ISOSCELES TRAPEZOID Trapezoid (Exactly one pair of parallel sides.) Non-parallel sides are congruent .

Example #1 a) Classify each figure in as many ways as possible, b) Determine the most precise name for each figure. A) B) C) quadrilateral quadrilateral quadrilateral trapezoid parallelogram rectangle parallelogram isosceles trapezoid rhombus square

Example #1 For the examples below, determine if the statement is “True” or “False”. (D) Every rectangle is a square. (E) Every isosceles trapezoid is a quadrilateral. False True

Example #2 A) The figure is a kite. x = _______ x + 2 2x – 1 2x – 1 = x + 2 x - 1 = 2 x = 3

Example #2 B) The figure is a rectangle. m = _______ Each angle of a rectangle is 90 (12m – 6)0 12m – 6 = 90 12m = 96 m = 8

Example #2 x = 20 C) The figure is a parallelogram. x = _______ Opposite sides are parallel. (4x – 5)0 (2x + 65)0 Same-side interior angles are supplementary 2x + 65 + 4x – 5 = 180 6x + 60 = 180 6x = 120 x = 20

Example #2 3b + 2 5a + 4 4b – 2 3a + 8 D) The figure is a rhombus. All sides are equal. 5a + 4 = 3a + 8 2a = 4 a = 2 4b – 2 = 3b + 2 b = 4

MG = 5/7 GB -9/0 = Und. BD 1/7 DM -5/0 = Und. 6 – 1 4 – (-3) -3 – 6 Example #3 A) Vertices: M(-3, 1), G(4, 6), B(4, -3), D(-3, -4) The figure appears to be a …. M G B D Trapezoid Let’s prove it … Side Slopes: MG GB BD DM = 5/7 -9/0 = Und. 1/7 -5/0 = Und. 6 – 1 4 – (-3) -3 – 6 4 – 4 -4 – (-3) -3 – 4 One Pair of Parallel sides. -4 – 1 -3 – (-3)

Example #3 4 – 0 -1 – 5 1 – -3 -3 – 3 4 – 1 -1 – -3 -3 – 0 3 – 5 B) Vertices: T(-1, 4), A(5, 0), J(3, -3), W(-3, 1) The figure appears to be a …. RECTANGLE T A J W Let’s prove it … Slopes: TA = WJ = TW = JA = = 4/-6 = -2/3 = 3/2 = -3/-2 = 3/2 4 – 0 -1 – 5 1 – -3 -3 – 3 Slopes of adjacent side lengths are opposite reciprocals, so sides form right angles. TAJW is a rectangle. 4 – 1 -1 – -3 -3 – 0 3 – 5

Homework Time!