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**1.6 Classifying Quadrilaterals**

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

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**1.6 Classifying Quadrilaterals**

What is a Quadrilateral? A polygons with exactly four sides

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**Special Quadrilaterals**

Quadrilaterals with specific characteristics. Parallelogram Rectangle Rhombus Square Trapezoid Kite

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

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Rhombus Rhombus: A parallelogram with four congruent sides

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Rectangle Rectangle: A parallelogram with four right angles

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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

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

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

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**Quadrilateral Family Tree**

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**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.

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**Classifying Quadrilaterals**

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

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**Classifying Quadrilaterals**

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

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**Classifying Quadrilaterals**

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

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**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

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**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

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**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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Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.

Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.

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