Similar Figures 61B - LCPS
61BSimilar FiguresVocabularySymbolDefinitionExample ABCDE HIJ Things to remember when figures are similar:1) ONLY the angles are congruent2) Side lengths are proportionalCircle all the true statements regarding the similar figures represented below.
Similar FiguresSteps to determine if two figures are similar:1) Take the first set of corresponding sides and write them as the first fraction of theproportion2) Take the other set of corresponding sides and write them as the second fraction of theproportion.3) Cross multiply4) If it forms a true proportion (the fractions are equivalent) then the figures are similar.1. If ABC is similar to ADE, then𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ?𝐴𝐴𝐴𝐴.Which segment replaces the “?” to makethe statement true?2. This is a pair of similar triangles. Which ofthe following proportions is true for thesetriangles?𝑎𝑎𝑐𝑐a. b.𝑎𝑎c.𝑎𝑎d.𝑎𝑎Steps to find a missing measurement:1) Determine the corresponding sides2) Set up a proportion3) Cross multiply to solve for the missing length4) Label your answer and check your work1. Two rectangles are similar. Which proportioncould you solve to find the missing side length?a.b.c.d.4154𝑥𝑥𝑥𝑥 154 1522.5𝑥𝑥22.5 � ��𝑏2. What must the value of x be in order for thefigures below to be similar?
Similar Figures PracticeDetermine if the two figures are similar.1. L 4 in M2.V5 cmQ 2 in R12 inO3.E6 inIH3 kmVX5 inTZ2 kmG25 in2 inYCB6. What must the value of x be in order forthe figures below to be similar?C72cm57 inJ24 inxK8 ftA10 inUFind the missing measurement.5. What must the value of x be in order forthe figures below to be similar?xXYA1 km5 kmB2 cmSJH10 cm1 cmG4.IWFSTNUDM18 cm12 cmL7. What must the value of x be in order forthe figures below to be similar?8. What must the value of x be in order forthe figures below to be similar?x14 mmx10 ft75 ft15 ft68 mm17 mm
9. Hakan is standing next to a buildingwhose shadow is 15 feet long. If Hakan is6 feet tall and is casting a shadow 2.5 feetlong, how high is the building?10. Find the value of d in the similar polygonsbelow.1.5 ftd4.05 ft7.29 ft11. Find the value of x in the polygons below. 12. What must the value of x be in order forthe figures below to be similar?4 ydx0.66 yd1.5 yd13. Use the similar triangles below to find the 14.The tallest tree in the United States is aheight of the tree.Coast Redwood in Jedidiah Smith StatePark in California. It is 321 feet tall.Suppose you are 5 feet 8 inches tall andcast a shadow that is 2 feet at a certaintime of day. About how long is the tree’sshadow at the same time of day? (convertH ft5 ft 8 inches to feet)5.5 ft3 ft24 ft
Similar Figures HomeworkFind the value of x in each pair of similar figures.DB1)1)3 ft6 ftAC4 ftEFXB2)FC18 ft2)X12 ftJGAD14 ftHLQ3)15 in20 inMR3)12 inXSTNO
Read and solve each problem carefully. Draw pictures to help you!4) The length and width of a rectangular box 5) The sides of two triangles are in the ratioare 10 in. and 8 in., respectively. Anotherof 1:2. If the length of the sides of the firstrectangular box has a length of 15 in. and atriangle are 5 cm, 9 cm, and 11 cm, what arewidth of 12 in. respectively. Are the lengththe lengths of the sides of the secondand width dimensions of the two rectangular triangle?boxes similar?6) A tree casts a shadow 60 feet long. At the 7) A grain silo casts a shadow of 40 feetsame time, a nearby 8-foot post casts a 12while a nearby fence post casts a shadow offoot shadow. How tall is the tree?2 feet. The fence post is 5 feet high. Howtall is the grain silo?8) If Quadrilateral DOGS is similar toQuadrilateral BEAR, thenAGSAR DOBEBDOBE SDARCOGAR DSBRDSDOG AREA9) Triangle ABC is similar to triangle PQR.Which proportion can be used to find n?
Find the missing measurement. 5. What must the value of . x. be in order for the figures below to be similar? 6. What must the value of . x be in order for the figures below to be similar? 7. What must the value of x be in order for the figures below to be similar? 8. What must the value of x be in order for the figures below to be similar? L M
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Form JFB-E1 Request for Change of School Assignment is available on the LCPS website or at any school LCPS Policies JFB & IKE MIDDLE SCHOOL MAGNET PROGRAMS Magnet programs are specific to LCPS middle schools. A magnet school is a school which offers specialized courses or curricula in a particular field of study.
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Dr. Patricia D. Nelson Director 571-252-1067 patricia.d.nelson@lcps.org Office of Special Education . Supervisor 571-252-1885 jennifer.evans@lcps.org Student Assistance Services Becky Hicks Specialist . Specialized Music Instruction Dr. Joy Engstrom Supervisor 571-252-1232 joy.engstrom@lcps.org Woodgrove High
The List of Figures is mandatory only if there are 5 or more figures found in the document. However, you can choose to have a List of Figures if there are 4 or less figures in the document. Regardless of whether you are required to have a List of Figures or if you chose
similar fi gures, p. 196 corresponding angles, p. 196 corresponding sides, p. 196 Similar Figures Figures that have the same shape but not necessarily the same size are called similar fi gures. The triangles below are similar. E D F B A C Matching angles are called correspondi
Section 2.5 Similar Figures 73 EXAMPLE 2 Finding an Unknown Measure in Similar Figures The triangles are similar. Find x. Because the triangles are similar, corresponding side lengths are proportional. So, write and solve a proportion to fi nd x. 6 — 9 8 — x Write a proportion. 6x 72
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