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Transcript
Math 9 Numeracy – Unit 7.7 - Geometry Review 7.7 – Geometry Review During the course of this unit we have examined the basic geometric shapes, angles, triangles, perimeters and areas of both rectangles and circles. You have also examined how to interpret and create circle graphs. This review package will go over all of these concepts and will provide you with some practice questions in order to prepare you for your unit exam. Here are the basic geometric shapes you will have to know; You will also need to know these lines. Identifying Angles An angle is made up of two rays that meet at a point know as a vertex. Point A is the vertex of angle BAC. Line AB and Line AC meet at Point A. Lines are identified by two points, as in Line AB. Angles are identified by three points with the middle point always being the vertex as in Angle BAC. An angle is measured in terms of a unit knows as a “degree” ( o). There are 360 o in a circle. Here are some common angles; Triangles A triangle consists of three connecting line segments enclosing three angles. Each triangle can be classified by the type of angles that it contains; or by their sides; Measuring the Angles in a Triangle You MUST remember that if you were to add up all the angles within a triangle the sum would equal 1800. That means that if you knew what two of the angles were, you could always solve for the third by subtracting the other two from 180. Perimeter The perimeter of a shape is simply the total distance AROUND the shape. To calculate the perimeter, simply measure the sides, and add up those measurements. Examine the following examples; Area The space within a shape is called area. The area of a square and a rectangle use the formula; Area = base x height or A = b x h For example; Finding the Area of a Parallelogram Finding the area of a parallelogram is a bit trickier only because the sides of a parallelogram are usually at a slant. In order to find the height that can then be used in your formula A = B x H, you have to find the height as it relates to a right angle. Almost all questions that you come across that ask you to calculate the area of a parallelogram; will somehow make that right-angle height known to you. You may have to look for it, but it will be there. *Note* When calculating the area of a parallelogram your height is always found by the right-angle measurement. NOT the length of the slanted side! Finding the Area of a Triangle To calculate the area of a triangle, you have to use a different formula. That is because a triangle is essentially one half of a rectangle. Because a triangle is half of a rectangle you simple take the formula for a rectangle ( A = B x H ) and divide it by 2. Circumference Like perimeter, the circumference of a circle is the distance AROUND the outside. Unlike an object with straight side, the circumference of a circle is more difficult to calculate, in fact, you need a formula to solve the circumference of a circle. In order to use the formula for the circumference of a circle, you have to know two terms as they relate to a circle; the diameter and the radius. The diameter is the straight line, from one side of the circle through the next, straight through the middle. The radius is a straight line, staring from the middle and extending out to a side. In order to solve the problem of calculating the circumference of a circle we have to use a very specific ratio which in this case is called pi and is represented by the Greek symbol; Pi has a value of 3.14 Because the radius is half the size of the diameter, the formula for the circumference (c) can either be expressed using radius (r) or diameter (d); Area of a Circle The area of a circle is simply the amount of space contained within a circle. Like all other area questions, answers are ALWAYS in “units squared” such as cm2 or in.2. Study the example questions provided below; Interpreting Circle Graphs A circle graph is sometimes called a pie graph. It shows how a total amount has been divided into parts according to percents. The percents of a circle graph always add up to 100%. The following circle graph shows the inventory at Future Shop, an electronics superstore. Calculating Amounts from Circle Graph Percents Because circle graphs are expressed as percents of an amount, the specific amount can be calculated by multiplying the decimal form of the percent (always use the decimal form of a percent when you use calculations) by the total amount the pie graph is representing. For example; What is the new inventory dollar amount that Future Shop has in computer stock? Solution: Circle Graphs Pie graphs are another way of representing information in a graphical, but easy to understand manner. Pie graphs convert percentages into degrees and then map out “pieces of pie” in a circle. For example, if you had a data table that had collected information on what a group of 200 people thought were Mr. Trickey’s best attributes, it may look something like this; Mr. Trickey’s Attributes His athletic prowess 36 His sense of humour 18 His rugged good looks 54 His keen fashion sense 10 His ability to attract “the ladies” 82 Total People Interviewed 200 In order to convert this data into a pie graph we must first convert the data into a percentage and then multiply that percentage by 360. We multiply by 360 because there are 360 degrees in a complete circle. Once we have converted our data into degrees we can then use a protractor to draw our pie graph. Mr. Trickey’s Attributes Data Convert to % His athletic prowess 36 36/200 = 18% His sense of humour 18 18/200 = 9% His rugged good looks 54 54/200 = 27% His keen sense of fashion 10 10/200 = 5% His ability to attract “the ladies” 82 72/200 = 41% Totals 200 100% Convert to Degrees 0.18 x 360 = 65 degrees 0.09 x 360 = 32 degrees 0.27 x 360 = 97 degrees 0.05 x 360 = 18 degrees 0.41 x 360 = 148 degrees 360 Degrees We can then use a protractor to map out and then label our pie graph to look like this; Fashion Sense Athletic Prowess Humour Good Looks Ability to attract “the ladies” Math 7 – Unit 7.7 Geometry Review 7.7 – Geometry Review - Practice Questions Directions: Name the following shapes; _______________ ________________ _______________ Directions: Name the following angles; _______________ Directions: Find the following angles; Angle A = _______ Angle B = _______ Angle C = _______ ________________ _______________ Angle X = _______ Angle Y = _______ Angle Z = _______ Directions: Name the following type of triangle; ___________________ ___________________ _________________ ___________________ _________________ Directions: Find the missing angles __________________ Directions: Find the perimeter of the following shapes; Show all your work for full marks! Directions: Calculate the following areas. Start with the formula and then show all your work for full marks! Directions: Use the information provided to complete the data table and then use a protractor to create an accurate circle graph. Favourite Type of Ice Cream Data Convert to a % Convert to Degrees Activity Chocolate 125 Vanillia 160 Strawberry 75 Tiger 50 Bubble Gum 90 Total 100% 3600 Title of graph: Title of graph: Cut out the protractor provided and starting at 0 degrees measure out your “pie pieces” according to your calculations above