How to define and classify special types of quadrilaterals. Chapter 6.1GeometryStandard/Goal 2.2, 4.1

1. Work on Test Analysis for Chapter 3.5 & Chapter Read, write, and discuss how to define and classify special types of quadrilaterals. 3. Work on assignment.

Polygon Is a closed figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear. Quadrilateral A polygon with four sides.

Parallelogram is a quadrilateral with both pairs of opposite sides parallel.

rhombus is a parallelogram with four congruent sides.

rectangle is a parallelogram with four right angles.

square is a parallelogram with four congruent sides and four right angles.

kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.

trapezoid is a quadrilateral with exactly one pair of parallel sides.

Isosceles trapezoid is a quadrilateral with exactly one pair of parallel sides and whose nonparallel opposite sides are congruent.

ABCD is a quadrilateral because it has four sides. Judging by appearance, classify ABCD in as many ways as possible. It is a trapezoid because AB and DC appear parallel and AD and BC appear nonparallel.

Determine the most precise name for the quadrilateral with vertices Q (–4, 4), B (–2, 9), H (8, 9), and A (10, 4). Graph quadrilateral QBHA. First, find the slope of each side. slope of QB = slope of BH = slope of HA = slope of QA = 9 – 4 –2 – (–4) 5252 = 9 – 9 8 – (–2) = 0 4 – 9 10 – 8 = – – 4 –4 – 10 = 0 BH is parallel to QA because their slopes are equal. QB is not parallel to HA because their slopes are not equal.

Because QB = HA, QBHA is an isosceles trapezoid. One pair of opposite sides are parallel, so QBHA is a trapezoid. Next, use the distance formula to see whether any pairs of sides are congruent. (continued) QB = ( –2 – ( –4)) 2 + (9 – 4) 2 = = 29 HA = (10 – 8) 2 + (4 – 9) 2 = = 29 BH = (8 – (–2)) 2 + (9 – 9) 2 = = 10 QA = (– 4 – 10) 2 + (4 – 4) 2 = = 14

In parallelogram RSTU, m R = 2 x – 10 and m S = 3 x Find x. Draw quadrilateral RSTU. Label R and S. RSTU is a parallelogram.Given Definition of parallelogram ST || RU m R + m S = 180 If lines are parallel, then interior angles on the same side of a transversal are supplementary. Lesson 6-1

(continued) Subtract 40 from each side. 5 x = x + 40 = 180 Simplify. x = 28 Divide each side by 5. (2 x – 10) + (3 x + 50) = 180Substitute 2 x – 10 for m R and 3 x + 50 for m S. Lesson 6-1

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.