Section 6-1 Classify Quadrilaterals SPI 32A: Identify properties of plane figures from information given in a diagram Objectives:

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Presentation transcript:

Section 6-1 Classify Quadrilaterals SPI 32A: Identify properties of plane figures from information given in a diagram Objectives: Define, classify and use properties of Quadrilaterals Recall Distance Formula: Slope Formula:

Types of Quadrilaterals Describe the Parallelogram Both pairs of opposite sides parallel.

Types of Quadrilaterals Describe the Rhombus Parallelogram with four congruent sides

Types of Quadrilaterals Describe the Rectangle Parallelogram with four right angles

Types of Quadrilaterals Describe the Square Parallelogram with four congruent sides and four right angles

Types of Quadrilaterals It is NOT a parallelogram! Describe the Kite Note: It is NOT a parallelogram! Quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

Describe the Trapezoid Types of Quadrilaterals Describe the Trapezoid Quadrilateral with exactly one pair of parallel sides The figure above is an Isosceles Trapezoid. (nonparallel opposite sides are congruent)

Types of Quadrilaterals Relationships among Quadrilaterals

Quadrilaterals can be classified by appearance: Classify Quadrilaterals Quadrilaterals can be classified by appearance: Judging by appearance, classify WXYZ in as many ways as possible. Quadrilateral, because it has four sides. Parallelogram, because both pairs of opposite sides are  Rhombus, because it has four congruent sides.

Classify Quadrilaterals by Coordinate Methods Determine the most precise name for quadrilateral LMNP. 1. Find the slope of each side to determine if sides are || or . How would you determine if the sides are parallel or Perpendicular? Both pairs of opposite sides are parallel, so LMNP is a parallelogram. (Slope is the same) 2. Use the distance formula to determine if any pairs of sides are congruent.

Use properties of Quadrilaterals to Find Values Given the figure below is a kite, find the values for x and y. Find the value of x. Justify each step. KB = JB Def of Kite 3x – 5 = 2x + 4 Substitute x – 5 = 4 Subtract 2x (SPE) x = 9 Add 5 (APE) Find the value of y. Justify each step. KT = JT Def of Kite 15 = 2y + 5 Substitute 10 = 2y Subtract 5 (SPE) 5 = y Divide (DPE)