5-7 similar figures and proportions course 2 warm up warm up problem of the day problem of the day...
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Warm UpProblem of the DayPresentation Six Lessons
Warm UpFind the cross products, then tell whether the ratios are equal.1.166,40152.38,18463.89,24274.2812,4218240 = 240; equal216 = 216; equal504 = 504; equal
Problem of the DayEvery 8th telephone pole along a road has a red band painted on it. Every 14th pole has an emergency call phone on it. What is the number of the first pole with both a red band and a call phone? 56
Lesson 1EQ: How can I determine if two figures are similar?
Vocabulary Wordssimilarcorresponding sidescorresponding anglesInsert Lesson Title Here
Octahedral fluorite is a crystal found in nature. It grows in the shape of an octahedron, which is a solid figure with eight triangular faces. The triangles in different-sized fluorite crystals are similar figures. Similar figures have the same shape but not necessarily the same size.
SIMILAR FIGURESTwo figures are similar ifThe measures of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.
Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.
Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.Example 1: Determining Whether Two Triangles Are SimilarACB10 in4 in7 inDEF16 in28 in40 inABDEBCEFACDF4167281040141414Since the ratios of the corresponding sides are equivalent, the triangles are similar.Step 1: Write ratios using the corresponding sides.Step 2: Substitute the length of the sides.Step 3: Simplify each ratio.
Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.Check It Out: Example 2ACB9 in3 in7 inDEF9 in21 in27 inABDEBCEFACDF39721927131313Since the ratios of the corresponding sides are equivalent, the triangles are similar.Write ratios using the corresponding sides.Substitute the length of the sides.Simplify each ratio.
Lesson 2EQ: How can I determine if figures are similar based on their angle measure?
Tell whether the figures are similar.How can I determine if these shapes are similar?Yes.The corresponding angles of the figures have equal measure.6060FAEDBC*remember the sum of the interior angles of a triangle = 180
Try One:Insert Lesson Title HereTell whether the figures are similar. (Notice the shapes are turned)1.similar
Try another:Insert Lesson Title HereTell whether the figures are similar.2.not similar
Lesson 3EQ: How can I determine the scale factor of similar figures?
Scale Factor:The ratio of the lengths of corresponding sides in similar figures
EXAMPLE 1The figures below are similarHow can I determine the scale factor of similar figures?34
EXAMPLE 2A ~ BHow can I determine the scale factor of similar figures?52.521AB
Lesson 4EQ: What is the relationship between the scale factor, side lengths, perimeter, and area?
The relationship between scale factor, side lengths, perimeter, and area...10 ft3 ft6 ft11 ft5.5 ft5 ft*The scale factor tells you the ratio of corresponding side lengths and the ratio of the perimeters
*The scale factor SQUARED tells you the ratio of the areas
FigureABRatio/Scale FactorCorresponding SidesSide Lengths (feet)PerimeterArea
Lesson 5EQ: How can I determine missing side lengths of similar figures?
Find the unknown length in similar figures.Example 1: Missing Side LengthsACQS=ABQRStep 1: Write a proportion using corresponding sides.1248=14wStep 2: Substitute lengths of the sides.12 w = 48 14Step 3: Cross multiply and divide.12w = 67212w12
=67212w = 56QR is 56 centimeters.Divide each side by 12 to isolate the variable.
Check It Out: Example 2 Insert Lesson Title HereABCD10 cm12 cmQRST24 cmACQS=ABQRWrite a proportion using corresponding sides.1224=10xSubstitute lengths of the sides.12 x = 24 10Find the cross product.12x = 240Multiply.12x12
=24012x = 20QR is 20 centimeters.Divide each side by 12 to isolate the variable.Find the unknown length in similar figures.x
The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.Insert Lesson Title HereLet x = the base of the inside triangle.82=12x8 x = 2 128x = 248x8
=248x = 3The base of the inside triangle is 3 inches.Write a proportion using corresponding sidelengths.Find the cross products.Multiply.Divide each side by 8 to isolate the variable.Example 3: Measurement Application
Example 4The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.Insert Lesson Title Here3 cm6 cm12 cmLet w = the width of the right rectangle.612=3w6 w = 12 36w = 366w6=366w = 6The right rectangle is 6 cm wide.Write a proportion using correspondingside lengths.Find the cross products.Multiply.Divide each side by 6 to isolate the variable.?
Ticket-out-the-doorFind the unknown length in each pair of similar figures.Insert Lesson Title Here1.2.
Ticket-out-the-doorFind the unknown length in each pair of similar figures.Insert Lesson Title Here3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake.
Lesson 6EQ: How can I use shadow math to find missing side lengths?
Step 1: Label Corresponding Parts.Step 2: Write a Proportion.Step 3: Cross multiply anddivide.x5m1m1.5mExample 1: Missing Side Lengths
Additional Example 2: Estimating with Indirect Measurement City officials want to know the height of a traffic light. Estimate the height of the traffic light.27.2515=48.75hStep 1: Label Corresponding Parts.9549hStep 2: Write a Proportion9h 245The traffic light is about 30 feet tall.27.25 ft48.75 fth ft271549hStep 3: Cross multiply.h 27Multiply each side by 9 to isolate the variable.
Check It Out: Example 3The inside triangle is similar in shape to the outside triangle. These are called NESTED triangles. Find the height of the outside triangle.514.75=h30.25Write a proportion.Use compatible numbers to estimate.13h30Simplify.1 30 3 hThe outside triangle is about 10 feet tall.14.75 ft30.25 fth ft515h3030 3hMultiply each side by 5 to isolate the variable.5 ftCross multiply.10 h
ClassworkProblem 5.1(pg.78-79)Problem 5.2 (pg. 80-81)Problem 5.3 (pg. 82-83)