This chapter opens with a set of explorations designed to introduce you to new geometric topics that you will explore further. You will learn about the special properties of a quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus. You will also develop a deeper understanding of the Pythagorean theorem. The chapter ends with an exploration of coordinate geometry.

In this chapter, you will learn: the relationships of the sides, angles, and diagonals of special quadrilaterals, such as parallelograms, rectangles, kites and rhombi (plural of rhombus) the Pythagorean theorem how to use algebraic tools to explore quadrilaterals on coordinate axes

3.1 How Can I Measure An Object? Pg. 3 Units of Measure

3.1 – How Can I Measure an Object?______ Units of Measure How tall are you? How large is the United States? How much water does your bathtub at home hold? All of these questions ask about size of objects around you. How can we answer these questions more specifically than saying "big" or "small"? Today you will be investigating ways to answer these and other questions like them.

3.1 – UNITS OF LENGTH Length often provides a direct way to answer the question, "How big?" In this activity, your teacher will give your team rulers with a unit of length to use to measure distances. For instance, if you have an object that has the same length as three of your units placed next to each other, then the object's length is "3 units."

a. Common units you may have used before are inches or meters. Today you are going to measure in inches or centimeters, based on your teachers assignment. Team Captains and Facilitators – Centimeters Reporters and Resource Managers – Inches

b. The dimensions of a figure are its measurement of length. For example, the measurement in each figure at right describe the relative size of each object.

Find the dimensions of the shape at right using your unit of length. That is, how wide is the shape? How tall? Compare your results with those of other teams.

c. The local baseball club is planning to make a mural that is the same general shape as the one you measured above. The club plans to frame the mural with neon tubes. Approximately how many units of neon tube will they need to do this?

3.2 – AREA To paint the mural, the wall must first be covered with a coat of primer. How much of the wall will need to be painted with primer? Remember that the measurement of the region inside a shape is called the area of the shape.

a. Because area measures the number of squares inside a shape, it is called "one square unit" and can be abbreviated as 1 un 2. What is the abbreviation for centimeters? cm 2

b. What is the approximate area of the mural? That is, how many of your square units fit within your shape?

c. When you answered part (b) did you count the squares? Did your team use a shortcut? If so, why does the shortcut work?

3.3 – SQUARE VS. RECTANGLE What do squares and rectangles have in common? What is different? Draw a picture of each, marking any important information on each. Then explain how to find the perimeter and area of each.

3.4 –COMPOSITE SHAPES Find the perimeter and/or total area of the shaded figures. Show all work.

= 18un (6)(3) = 18un 2

un

un 2

un un 2

un 324 un 2

256 un 2 (24)(12) – (8)(4)

3.5 – CONSTRUCTING PERPENDICULAR LINES THROUGH A POINT a. Examine the diagram at right. If a line was drawn from point P straight down to line l, would that bisect the line?

b. Place the point of the compass on P and leave a mark that crosses line l. You may have to extend line l to get two points of intersection. c. From the new points of intersection, leave a mark below the line, creating an X. d. Connect the intersection of part (c) to point P. This should be perpendicular to line l.

3.6 – CONSTRUCT A SQUARE Using the construction from the previous problem, create a square with the given side length. side length

SquareRectangle Area = side 2 Area = bh