Numerical & Geometric Proportions
Mathematics, Grade 7
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Numerical Proportions Geometric Proportions corresponding sides corresponding angles A B C D E F • Numerical Proportions compare two numbers. • Ratios are used to compare quantities with the same unit. • Rates are used to compare quantities measured with different units. • Cross products are used to find a missing quantity in a proportion. • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • Identify the corresponding sides in the two triangles. • Use ratios of the corresponding sides to determine whether the triangles ΔGHI and ΔJKL are similar. • The triangles are similar since their corresponding sides are equivalent. • A cross product is the product of the numerator in one ratio and the denominator in the other ratio. Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal. 3 6 1 2 = a b c d = m 5 12 4 = 4m 4 60 4 = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 = m • 4 5 • 12 = 4m 60 = m 15 • Cross multiply. • Divide each side by 4 to isolate the variable. Determining whether two triangles are similar G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm 4 16 6 24 = 3 12 = ? ? GH JK IH LK = IG LJ = ? ? 1 4 1 4 = 1 4 = • An equation with two equal ratios is called a proportion. © Copyright NewPath Learning. All Rights Reserved. 93-4704 www.newpathlearning.com GH corresponds to JK IH corresponds to LK IG corresponds to LJ Numerical & Geometric Proportions
Numerical Proportions Geometric Proportions • Numerical Proportions compare two numbers . • Ratios are used to compare quantities with the . • Rate s are used to compare quantities measured with different units. • are used to find a missing quantity in a proportion. • Geometric proportions compare two . • Similar figures have equal corresponding and corresponding that are in . • Identify the corresponding sides in the two triangles. • Use ratios of the corresponding sides to determine whether the triangles ∆GHI and ∆JKL are similar. • The triangles are similar since their corresponding sides are equiva lent. • A cross product is the product of the in in one ratio and the in the other ratio. 3 6 1 2 = Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal . a b c d = m 5 12 4 = 3 5 6 10 = 5 • 6 = 5 • 6 = = • • = = m 15 • Cross multiply. • Divide each side by to isolate the variable. A B C D E F Determining whether two triangles are similar • An equation with two equal ratios is called a proportion. G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm = © Copyright NewPath Learning. All Rights Reserved. 93-4704 www.newpathlearning.com Numerical & Geometric Proportions Key Vocabulary Terms • corresponding angle • corresponding side • cross multiply • cross product • denominator • equation • equivalent • geometric proportion • numerator • numerical proportion • proportion • rate • ratio • similar figure • triangle • variable GH corresponds to JK GH corresponds to JK GH corresponds to JK = = ? ? = = \|xiBAHBDy01678mzV
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