Similarity and scale
Mathematics, Grade 8
Similarity and scale
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Similarity and scale
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Similarity and scale
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Similarity and scale
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Similarity and scale
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Study Guide Similarity and scale Mathematics, Grade 8
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SIMILARITY AND SCALE Similarity refers to similar figures and the ability to compare them using proportions. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • A proportion equation can be used to prove two figures to be similar. • If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Scale refers to a comparison of two objects using a scale or direct unit of comparison. For example, maps use scales to measure the distance on a map and then compare it to how far the distance really is in real life. • Scale drawings and scale models also use proportion equations to determine missing information. • Scale drawings refer to maps, blueprints and the like. • Scale models refer to models of any life size objects whether it is buildings, cars, or planes for example. • A scale factor is used to compare a smaller version to a larger version of an object. As similar figures use ratios to find the measure of missing sides of a figure, trigonometric ratios can be used to find the measure of missing sides or angles of a right triangle. • The trigonometric ratios are sine, cosine and tangent. Each stands for a certain ratio that when used can determine the measure of a missing side or angle of a right triangle. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use similarity and scale When two figures are said to be similar, it means that their sides are in proportion and their angles are equal. If these two rectangles are similar, what is the length of the missing side? The proportion equation can be used to determine the missing side to be 3 m. It is important to make sure the proper sides of the figure match up with the proportion. Map scales and scale drawings also use proportion equations. If a map has a scale of 1 inch equal 5 miles, how far would 6.5 inches be? Ex. 5 miles = x miles (5)(6.5) = 1x 1 inch 6.5 inches 32.5 = x, so 6.5 inches equals 32.5 miles • With proportional equations, it is very important that the correct units are lined up in order to find the correct result. The same proportion equations can be use with scale models. Trigonometric ratios can be used to find the measure of missing sides or angles of a right triangle. The trigonometric ratios are sine, cosine and tangent. Each refers to a ratio of a right triangle. • The sine is the opposite side/hypotenuse. • The cosine is the adjacent side/hypotenuse. • The tangent is the opposite side/adjacent side. • This is often remembered by various sayings such as, Some Old Horse Caught Another Horse Taking Oats Away. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
To find the ratios, a certain angle must be specified. For example, what are the trigonometric ratios for angle A? • The trigonometric ratios can be used to solve for missing sides or angles. For example what is the length of the missing side of the triangle shown? What is the measure of angle B? To find the measure of sin 36°, u se a calculator. To find what angle B is, use a calculator to find the inverse sin of .3846, this will give the needed information to solve for angle B. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. Two rectangles are similar; what is the length of the missing side? 2. A map has a scale of 1/2 inch = 12 miles. If two cities are 65 miles apart, how far is that on a ruler? 3. A model truck has a length of 18 cm. If the scale is 1cm = 1.5 feet, what is the length of the real truck? 4. What is the measure of the missing side? What is the measure of angle A? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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