1.6 Classifying Quadrilaterals Homework: Lesson 1.6/1-13, 15-18 Quiz Friday on Lessons 1.5 – 1.7

1.6 Classifying Quadrilaterals What is a Quadrilateral? A polygons with exactly four sides

Special Quadrilaterals Quadrilaterals with specific characteristics. Parallelogram Rectangle Rhombus Square Trapezoid Kite

Parallelogram Parallelogram: A Quadrilateral with both pairs of opposite sides parallel

Rhombus Rhombus: A parallelogram with four congruent sides

Rectangle Rectangle: A parallelogram with four right angles

Square Square: A parallelogram with four congruent sides and four right angles (it is a rhombus and a rectangle) A Square is a Regular Parallelogram

Kite Kite: A quadrilateral with two pairs of consecutive congruent sides no opposite sides congruent no parallel sides

Trapezoid Trapezoid: A quadrilateral with exactly one pair of parallel sides Isosceles Trapezoid: Trapezoid with legs (nonparallel sides) congruent

Quadrilateral Family Tree

Special Quadrilaterals A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and right angles. A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. A trapezoid is a quadrilateral with exactly one pair of parallel sides. The isosceles trapezoid at the right is a trapezoid whose nonparallel sides (legs) are congruent.

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Square Rectangle Rhombus Parallelogram Quadrilateral Parallelogram Quadrilateral

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Rhombus Parallelogram Quadrilateral Trapezoid Quadrilateral

Classifying Quadrilaterals Judging by appearance, classify each quadrilateral in as many ways as possible: Kite Quadrilateral Rectangle Parallelogram Quadrilateral

Using Properties Find the value of the variables for the kite: T JB = KB 2x + 4 = 3x – 5 -x = -9 x = 9 x + 6 2y + 5 J K TK = 9 + 6 TK = 15 3x - 5 2x + 4 TJ => 2y + 5 = 15 2y = 10 y = 5 B

Using Properties Find the values of the variables for the rhombus: 3b + 2 = 4b -2 b = 4 5a + 4 3a + 8 5a + 4 = 3a + 8 2a = 4 a = 2 4b - 2

Lesson Quiz Complete each statement. 1. A quadrilateral with four right angles is a _________. 2. A parallelogram with four right angles and four congruent sides is a _______. 3. A figure with 4 sides and 4 angles is a ______. 4. Give the most descriptive name for this quadrilateral. square or rectangle square quadrilateral trapezoid

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