Lesson 6-4 Similar Figures and Proportions
 because the ratios of their matching sidesmade a proportion.In the last example, the triangles were similarWhat is the simplified form of all of these ratios?1510Their ratios were all equal.=128=96= L4OIs rectangle LMNO similar to rectangle HIJK?1010NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?1. Are the corresponding (matching)10angles congruent (the same size)?10Yes.NM4No.3HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?1. Are the corresponding (matching)2. Do the corresponding (matching) sidesform a proportion (make equal fractions)?angles congruent (the same size)?1010Yes.NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?Which side corresponds to LM?1010NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?Which side corresponds to MN?1010NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?Write the ratio of LM to HI:1010NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?Write the ratio of MN to IJ:1010NM43HK88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?Use cross multiplication to determineif the ratio LM:HI is equal to the ratio MN:IJ.1010108?NM4433HKYesNo88IJ3 L4OIs rectangle LMNO similar to rectangle HIJK?10 • 3 = 308 • 4 = 32if the ratio LM:HI is equal to the ratio MN:IJ.Use cross multiplication to determine101030 ≠ 32NM43HKNO!88IJ3 L4ONow answer the question:Is rectangle LMNO similar to rectangle HIJK?1010YesNoNM43HK88IJ3 L4ONow answer the question:Is rectangle LMNO similar to rectangle HIJK?2. The sides do not make a proportion.1. The angles are congruent.1010NO! NM43HK88IJ3 A860∘BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212120∘D60∘8CK460∘L120∘6120∘660∘N4M A860∘1. Are the corresponding angles congruent?BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212120∘Yes.No.D60∘8CK460∘L120∘6120∘660∘N4M A860∘2. Do the sides form a proportion?Complete this ratio:BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212120∘D60∘8C8K460∘L120∘6120∘660∘N4M AComplete this proportion:860∘2. Do the sides form a proportion?BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212120∘D60∘8C84K460∘=L120∘6120∘660∘N4M AAre the cross-productsequal?860∘2. Do the sides form a proportion?BIs parallelogram ABCD similar toparallelogram KLMN?120∘Yes.No.1212120∘D60∘8C84K460∘=L120∘6126120∘660∘N4M What is the cross-product?A860∘2. Do the sides form a proportion?BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212120∘D60∘8C84K460∘=L120∘6126120∘660∘N4M A860∘BIs parallelogram ABCD similar toparallelogram KLMN?120∘1212Yes.No.120∘D60∘8CK460∘L120∘6120∘660∘N4M Which side corresponds to YZ?CDABADXW Complete the proportion:YZ2= equivalent fractions to solve for YZ.Use cross multiplication orYZ2=1624YZ =  24DA12CB15Given thattrapezoid ABCD ~ trapezoid WZYX,find m.WmZ16YX 24DA12CB15Complete the proportion used to find m:Given thattrapezoid ABCD ~ trapezoid WZYX,find m.Wm1624Z16=YX 24DA12CB15Given thattrapezoid ABCD ~ trapezoid WZYX,find m.WmUse cross multiplication or equivalent fractions to find m.1624Z=16m12m = YX 24DA12CB15trapezoid ABCD ~ trapezoid WZYX,find YZ.Given thatWComplete the ratio for YZ:mZ16YXYZ 24DA12CB15trapezoid ABCD ~ trapezoid WZYX,find YZ.Given thatWComplete the proportion:mZ16YXYZ15= 24DA12CB15trapezoid ABCD ~ trapezoid WZYX,find YZ.Given thatUse cross-multiplication to find YZ.W15YZm=Z162416YYZ = X CGiven ∆ABC ~ ∆DEFFind n.1210AB11F6nDE5.5 Complete this proportion:CGiven ∆ABC ~ ∆DEFFind n.1210AB1110nF6n=DE5.5 Solve this proportion:Cn = Given ∆ABC ~ ∆DEFFind n.1210AB1110nF6n=DE5.5126 How long is side JL? How long is side JK?15 GOOD JOB!1015 How long is side KG? Complete the proportion:15t= t = Solve the proportion for t:15t=106
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