At the right is a polygon known as a trapezoid. The two parallel sides (horizontal in this case) of the trapezoid are called bases. b1b1 b2b2 b2b2 b1b1 Complete RC-41 a) Draw a copy of the first trapezoid immediately to the right of it, BUT draw it so that the first trapezoid is turned upside down and shares a common (equal) side with the first trapezoid. If you draw it correctly, the two bases will switch positions (that is, the top base will become the bottom and the bottom length will become the top base.) Label the bases. If your drawing is accurate you will now have a parallelogram whose base is b 1 + b 2.

b) Draw in a height of the parallelogram. Label it h. b1b1 b2b2 b2b2 b1b1 h = (14)5 = 70 u 2 = (b 1 + b 2 )h RC-41 A = bh c) Write an algebraic equation (using b’s and h’s) for the area of the parallelogram and give the numerical result in square units. = (10 + 4)5 d) Explain how you can figure out the area of one of the trapezoids. Show your result both algebraically and numerically. You can divide by two or multiply by ½. A = ½(b 1 +b 2 )h = ½(10 + 4)5 = 35 u 2 +1

Trapezoid: Quadrilateral with ONE pair of opposite sides parallel. b1b1 b2b2 h A = ½(b 1 + b 2 )h

Two lines that meet (intersect) to form a 90º angle. The small square indicates that the lines are perpendicular and that the angle measures 90º. Note: Once you have established one right angle with intersecting lines, you can establish four right angles. Two lines on a two-dimensional surface are that do not intersect (cross) no matter how far they are extended.       Note that all lines extend without limit. That is what the arrowheads indicate. The symbol for parallel is ||. In figures, pairs of arrows like >, >>, and >>> will mean that lines are parallel. Perpendicular lines: The symbol for perpendicular is . Parallel lines:

a p b r f e Which pairs of lines are parallel? k Lines:b & f,e & r,a & p

Any side of a two-dimensional figure can be used as a BASE (b). HEIGHT (h) is the perpendicular distance: a)In triangles, the HEIGHT is from the line of the base to the opposing vertex. Some books call the height an altitude. You may use either term. b) In quadrilaterals, the height is between two parallel sides or the lines containing those sides. b h b h

RC-43 Remember that the height must be perpendicular (at a right angle) to the base. The square corner of a 3 x 5 index card makes an excellent height (or right angle) locator. Just slide one edge of the card along the base as shown below. You have to slide the card along the line that contains the base... until the card touches the opposing vertex. Now take your pencil and draw in the height. base (b) Be sure to label it “h”! h

A) DIRECTIONS: For figure 1 through 8 on the resource page, draw a height to the side labeled base. Remember that the height must be perpendicular (at a right angle) to the base. Just slide one edge of the card along the base as shown below. RC-43 base (b) Note: The length of the base does NOT change…the red segment is an extension of the line of the base. h

RC-43 b It will be helpful to spin your paper so that the base of your triangle is at the bottom. A) DIRECTIONS: For figures 1 through 8, draw a height to the side labeled base. Remember that the height must be perpendicular (at a right angle) to the base. B) For figures 9, 10, and 11, draw a height from each vertex (labeled A, B, and C). You will have three heights in each figure.