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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