11-5 Areas of Similar Figures. For each pair of similar figures, find the area of the green figure. SOLUTION:

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1 The area of the green diamond 9 yd F each pair of similar figures, find the area of the green figure The scale fact between the blue triangle and the 1 green triangle The scale fact between the blue diamond and the green diamond The area of the green triangle 784 m The area of the green diamond 9 yd F each pair of similar figures, use the given areas to find the scale fact from the blue to the green figure Then find x 3 The scale fact between the blue triangle and the green triangle The scale fact between the blue triangle and the green triangle The area of the green triangle 784 m F each pair of similar figures, use the given Page 1 The scale fact

2 The area of the green triangle 784 m F each pair of similar figures, use the given areas to find the scale fact from the blue to the green figure Then find x 4 The scale fact between the blue trapezoid and the 3 The scale fact between the blue triangle and the green trapezoid green triangle The scale fact The scale fact 5 MEMORIES Zola has a picture frame that holds all of her school pictures Each small opening similar to the large opening in the center If the center opening has an area of 33 square inches, what the area of each small opening? 4 The scale fact between the blue trapezoid and the green trapezoid The scale fact between the center opening and the small opening Page

3 F each pair of similar figures, find the area of the green figure 5 MEMORIES Zola has a picture frame that holds all of her school pictures Each small opening similar to the large opening in the center If the center opening has an area of 33 square inches, what the area of each small opening? 6 The scale fact between the blue triangle and the green triangle The scale fact between the center opening and the small opening The area of the green triangle 81 mm F each pair of similar figures, find the area of the green figure 7 The scale fact between the blue parallelogram and 6 the green parallelogram The scale fact between the blue triangle and the green triangle their areas, so the ratio of The area of the green parallelogram 40 ft Page 3 The area of the green triangle 81 mm

4 The area of the green parallelogram 40 ft The area of green pentagon 67 cm CCSS STRUCTURE F each pair of similar figures, use the given areas to find the scale fact of the blue to the green figure Then find x 8 The scale fact between the blue trapezoid and the green trapezoid 10 The scale fact between the blue figure and the green figure The area of green triangle 1515 in 9 The scale fact The scale fact between the blue pentagon and the green pentagon areas, so the ratio of their 11 The area of green pentagon 67 cm The scale fact between the blue triangle and the green triangle CCSS STRUCTURE F each pair of similar figures, use the given areas to find the scale fact of the blue to the green figure Then find x Page 4

5 11 The scale fact between the blue triangle and the green triangle 1 The scale fact between the blue figure and the green figure The scale fact The scale fact 1 13 The scale fact between the blue figure and the The scale fact between the blue figure and the green figure green figure Page 5

6 14 CRAFTS Marina crafts unique trivets and other kitchenware Each trivet an equilateral triangle The perimeter of the small trivet 9 inches, and the perimeter of the large trivet 1 inches If the area of the small trivet about 39 square inches, what the approximate area of the large trivet? 13 The scale fact between the blue figure and the green figure Since the given triangles are equilateral, the sides are congruent The perimeter of the small trivet 9 inches, so the length of each side of the small trivet 3 inches The perimeter of the large trivet 1 inches, so the length of each side of the large trivet 4 inches The scale fact between the small trivet and the large trivet The scale fact 14 CRAFTS Marina crafts unique trivets and other kitchenware Each trivet an equilateral triangle The perimeter of the small trivet 9 inches, and the perimeter of the large trivet 1 inches If the area of the small trivet about 39 square inches, what the approximate area of the large trivet? Since the given triangles are equilateral, the sides are congruent The perimeter of the small trivet 9 inches, so the length of each side of the small trivet 3 inches The perimeter of the large trivet 1 inches, so the length of each side of the large trivet 4 inches The scale fact between the small trivet and the 15 BAKING Kaitlyn wants to use one of two regular hexagonal cake pans f a recipe she making The side length of the larger pan 45 inches, and the area of the base of the smaller pan 416 square inches a What the side length of the smaller pan? b The recipe that Kaitlyn using calls f a circular cake pan with an 8-inch diameter Which pan should she choose? Explain your reasoning a Area of the smaller pan = 416 We know that the area of the regular hexagon where s the length of the side, APage 6 the area, and n the number of sides large trivet So, the area of large trivet 69 in

7 pan with an 8 in diameter about she choose? Explain your reasoning of the larger pan Area of of Similar the smaller pan = aAreas Figures We know that the area of the regular hexagon where s the length of the side, A the area, and n the number of sides The interi angle of a hexagon 60 and the apothem bects the side length creating a triangle with a shter leg that measures The length of the apothem therefe The area, and the area of the smaller pan The area of the larger pan closer to the area of the circle, so Kaitlyn should choose the larger pan to make the recipe 16 CHANGING DIMENSIONS A polygon has an area of 144 square meters a If the area doubled, how does each side length change? b How does each side length change if the area tripled? c What the change in each side length if the area increased by a fact of x? a Let A be the iginal area The the new area A From theem 111: b The area of the circular pie pan If the area doubled, each side length will increase by a fact of b Let A be the iginal area The the new area 3A From theem 111: The area of the smaller pan given 416 in, and the area of the larger pan can be determined using ratios If the area tripled, each side length will increase by a fact of c Let A be the iginal area The the new area The larger pan should be used since the larger pan closer to the area of the circular pan a 4 in b Larger; sample answer: The area of a circular pie pan with an 8 in diameter about The area of the larger pan, and the area of the smaller pan The area of the larger pan closer to the area of the circle, so Kaitlyn should choose the larger pan to make the recipe 16 CHANGING DIMENSIONS A polygon has an area of 144 square meters a If the area doubled, how does each side length xa From theem 111: If the area changes by a fact of x, then each side length will change by a fact of a If the area doubled, each side length will increase by a fact of Page 7 b If the area tripled, each side length will increase by a fact of

8 If the area changes by a fact of x, then each side length will change by a fact of a If the area doubled, each side length will increase by a fact of b If the area tripled, each side length will increase by a fact of c If the area changes by a fact of x, then each side length will change by a fact of 17 CHANGING DIMENSIONS A circle has a radius of 4 inches a If the area doubled, how does the radius change? b How does the radius change if the area tripled? c What the change in the radius if the area increased by a fact of x? a Let A be the area The new area A From theem 111: If the area tripled, the radius changes from 4 in to 416 in c Let A be the area The new area xa From theem 111: If the area changes by a fact of x, then the radius changes from 4 in to 4 in a If the area doubled, the radius changes from 4 in to 339 in b If the area tripled, the radius changes from 4 in to 416 in c If the area changes by a fact of x, then the radius changes from 4 in to 4 in 18 CCSS MODELING Federico s family putting hardwood flos in the two geometrically similar rooms shown If the cost of floing constant and the floing f the kitchen cost $000, what will be the total floing cost f the two rooms? Round to the nearest hundred dollars If the area doubled, the radius changes from 4 in to 339 in b Let A be the area The new area 3A From theem 111: The scale fact between the living room and kitchen If the area tripled, the radius changes from 4 in to 416 in c Let A be the area The new area xa From theem 111: Page 8

9 in to 339 in b If the area tripled, the radius changes from 4 in to 416 in If theof area changes by a fact of x, then the 11-5cAreas Similar Figures radius changes from 4 in to 4 in 18 CCSS MODELING Federico s family putting hardwood flos in the two geometrically similar rooms shown If the cost of floing constant and the floing f the kitchen cost $000, what will be the total floing cost f the two rooms? Round to the nearest hundred dollars $7600 COORDINATE GEOMETRY Find the area of each figure Use the segment length given to find the area of a similar polygon 19 The scale fact between the living room and kitchen Area of triangle JKL = 05(5)(6) 15 and The scale fact between $7600 COORDINATE GEOMETRY Find the area of each figure Use the segment length given to find the area of a similar polygon area of ; area of 0 19 Page 9

10 11-5area Areas of of Similar Figures ; area of area of WXYZ = 30 area of 1 0 Here, XY = WZ = 5 and WX = YZ = 6 Area of the rectangle WXYZ = 5(6) 30 Given that and The scale fact between rectangle quadrilateral the ratio of their areas, so Area of a triangle = ½ bh Substitute Area of triangle 6 Area of triangle 1 Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC = = 18 F the length of BC use the dtance fmula B = ( 3, 7) and C = ( 1, 5) area of WXYZ = 30 area of 1 Here, BC The scale fact between quadrilateral quadrilateral of their areas and, so the ratio Page 10

11 Here, BC and The scale fact between quadrilateral quadrilateral, so the ratio of their areas area of ABCD = 18 area of PROOF Write a paragraph proof Given: Prove: area of ABCD = 18 area of We wh to prove that the ratio of the areas of two similar triangles equal to the square of the ratios of cresponding side lengths Begin by using the fmula f the area of a triangle to compare the two areas in terms of their bases and heights Then use the fact that the triangles are similar to make a substitution f the cresponding ratio PROOF Write a paragraph proof Given: Prove: and the area of The area of The ratio of their areas Since the triangles are We wh to prove that the ratio of the areas of two similar triangles equal to the square of the ratios of cresponding side lengths Begin by using the fmula f the area of a triangle to compare the two areas in terms of their bases and heights Then use the fact that the triangles are similar to make a substitution f the cresponding ratio Therefe, by substitution similar, we have the following equation f the ratio and the area of cresponding measures are = = Therefe, by substitution The Manual area of- Powered by Cognero esolutions The ratio of the side the Since the triangles are Therefe, by substitution The ratio of the area of The ratio of their areas of cresponding side measures of cresponding side measures The area of and the area of The area of similar, we have the following equation f the ratio and the area of The ratio of the area of 3 STATISTICS The graph shows the increase in high school tenn participation from 1995 to 005 a Explain why the graph mleading b How could the graph be changed to me Page 11 accurately represent the growth in high school tenn participation?

12 Therefe, by substitution 3 STATISTICS The graph shows the increase in high school tenn participation from 1995 to 005 a Explain why the graph mleading b How could the graph be changed to me accurately represent the growth in high school tenn participation? a Sample answer: The graph mleading because the tenn balls used to illustrate the number of participants are similar circles When the diameter of the tenn ball increases, the area of the tenn ball also increases The ratio of the areas of the similar circles equal to the square of the ratio of their diameters F instance, if the diameter of one circle double another, then the ratio of their diameters :1 and the ratio of their areas 4:1Thus, the increase in area greater than the increase in the diameter Since the area of the tenn ball increases at a greater rate than the diameter of the tenn ball, it looks like the number of participants in high school tenn increasing me than it actually high school tenn increasing me than it actually b Sample answer: If you use a figure with a constant width to represent the participation in each year and only change the height, the graph would not be mleading 4 MULTIPLE REPRESENTATIONS In th proble proptionally in three-dimensional figures a TABULAR Copy and complete the table below f inches by 3 inches by 5 inches b VERBAL Make a conjecture about the relationsh scaled volume to the initial volume c GRAPHICAL Make a scatter plot of the scale fa initial volume using the STAT PLOT feature on your feature to approximate the function represented by th d ALGEBRAIC Write an algebraic expression f in terms of scale fact k a F the table, each dimension (length, width, hei volume will be the product of all the dimensions b Since each dimension being multiplied by a scal b Sample answer: If you use a figure with a constant width to represent the participation in each year and only change the height, the graph would not be mleading F example, use stacks of tenn balls of the same size to represent the number of participants f each of the years simply use bars of the same width Be sure to keep the scale the same a Sample answer: The graph mleading because the tenn balls used to illustrate the number of participants are similar circles When the diameter of the tenn ball increases, the area of the tenn ball also increases Since the area of the tenn ball increases at a greater rate than the diameter of the tenn ball, it looks like the number of participants in high school tenn increasing me than it actually b Sample answer: If you use a figure with a constant width to represent the participation in each year and only change the height, the graph would not be mleading esolutions Manual - Powered by Cognero 4 MULTIPLE REPRESENTATIONS In th proble proptionally in three-dimensional figures multiplying these terms together, we should suspect volume will be much larger than a simple linear relati c Enter the scale facts into L1 of your calculat, a into L Create a scatter plot using the L1, points as your x-va Page 1 Choose a suitable window and create a graph

13 Create a scatter plot using the L1, points as your x-va As we can see the R value f the cubic and quarti they fit the data exactly However the a, c, d, and e (the calculat reads as 0, which only 3 highest term x A cubic regression best fits the d Choose a suitable window and create a graph d a Then press STAT, CALC, and check different regr b Sample answer: The ratio increases at a greater ra linear c d 5 CCSS CRITIQUE Violeta and Gavin are trying to come up with a fmula that can be used to find the area of a circle with a radius r after it has been enlarged by a scale fact k Is either of them crect? Explain your reasoning As we can see the R value f the cubic and quarti they fit the data exactly However the a, c, d, and e Neither; sample answer: In der to find the area of the enlarged circle, you can multiply the radius by the scale fact and substitute it into the area fmula, you can multiply the area fmula by the scale fact squared The fmula f the area of the enlargement Page 13

14 Th would have been crect if the circle was increased by the scale fact, and not the radius d 5 CCSS CRITIQUE Violeta and Gavin are trying to come up with a fmula that can be used to find the area of a circle with a radius r after it has been enlarged by a scale fact k Is either of them crect? Explain your reasoning Neither; sample answer: In der to find the area of the enlarged circle, you can multiply the radius by the scale fact and substitute it into the area fmula, you can multiply the area fmula by the scale fact squared The fmula f the area of the enlargement Gavin took the square of the radius to the kth power 6 CHALLENGE If you want the area of a polygon to be x% of its iginal area, by what scale fact should you multiply each side length? We want: From theem 111 Combining these two, we have Neither; sample answer: In der to find the area of the enlarged circle, you can multiply the radius by the scale fact and substitute it into the area fmula, you can multiply the area fmula by the scale fact squared The fmula f the area of the enlargement Violeta multiplied the entire area by the scale fact Th would have been crect if the circle was increased by the scale fact, and not the radius Gavin took the square of the radius to the kth power 6 CHALLENGE If you want the area of a polygon to be x% of its iginal area, by what scale fact should you multiply each side length? We want: 7 REASONING A regular n-gon enlarged, and the ratio of the area of the enlarged figure to the area of the iginal figure R Write an equation relating the perimeter of the enlarged figure to the perimeter of the iginal figure Q Since we have a regular polygon with n sides, and a perimeter of Q, the side length of the polygon We know from theem 111 that if the scale fact f the areas R, then the scale fact f cresponding sides From theem 111 scaled polygon, so the side length of the The enlarged polygon still regular and has n sides so the perimeter of the enalrged polygon Combining these two, we have P enlarged = Page 14 8 OPEN ENDED Draw a pair of similar figures with areas that have a ratio of 4:1 Explain

15 P enlarged = 7 REASONING A regular n-gon enlarged, and the ratio of the area of the enlarged figure to the area of the iginal figure R Write an equation relating the perimeter of the enlarged figure to the perimeter of the iginal figure Q Since we have a regular polygon with n sides, and a perimeter of Q, the side length of the polygon We know from theem 111 that if the scale fact f the areas R, then the scale fact f cresponding sides scaled polygon, so the side length of the 8 OPEN ENDED Draw a pair of similar figures with areas that have a ratio of 4:1 Explain Sample answer: Draw two similar rectangles Since the ratio of the areas should be 4:1, the ratio of the lengths of the cresponding sides will be :1 Since, draw a rectangle with a width of 05 inches and a length of 1 inch and a second rectangle with a width of 1 inch and a length of inches Thus, a 05-inch by 1-inch rectangle and a 1inch by -inch rectangle are similar, and the ratio of their areas 4:1 The enlarged polygon still regular and has n sides so the perimeter of the enalrged polygon Sample answer: Since the ratio of the areas should be 4:1, the ratio of the lengths of the sides will be P enlarged = 8 OPEN ENDED Draw a pair of similar figures with areas that have a ratio of 4:1 Explain Sample answer: Draw two similar rectangles Since the ratio of the areas should be 4:1, the ratio of the lengths of the cresponding sides will be :1 Since, draw a rectangle with a width of 05 inches and a length of 1 inch and a second rectangle with a width of 1 inch and a length of inches Thus, a 05-inch by 1-inch rectangle and a 1inch by -inch rectangle are similar, and the ratio of their areas 4:1 Sample answer: Since the ratio of the areas should be 4:1, the ratio of the lengths of the sides will be :1 Thus, a 05-inch by 1-inch rectangle and a 1-inch by -inch rectangle are similar, and the ratio of their areas 4:1 :1 Thus, a 05-inch by 1-inch rectangle and a 1-inch by -inch rectangle are similar, and the ratio of their areas 4:1 9 WRITING IN MATH Explain how to find the area of an enlarged polygon if you know the area of the iginal polygon and the scale fact of the enlargement By theem 111 the ratio of the areas of a scaled polygon and its iginal equal to the square of the scale fact If you know the area of the iginal polygon and the scale fact of the enlargement, you can find the area of the enlarged polygon by multiplying the iginal area by the scale fact squared F example, if a triangle has an area of 10 and a similar triangle created by scaling each side of the iginal triangle by, then the area of the new triangle will be Sample answer: If you know the area of the iginal polygon and the scale fact of the enlargement,page you15 can find the area of the enlarged polygon by multiplying the iginal area by the scale fact squared

16 ratio of their areas 4:1 Sample answer: If you know the area of the iginal polygon and the scale fact of the enlargement, you can find the area of the enlarged polygon by multiplying the iginal area by the scale fact squared 9 WRITING IN MATH Explain how to find the area of an enlarged polygon if you know the area of the iginal polygon and the scale fact of the enlargement 30 the area of of A, AC = 15 inches, PT = 6 inches, and 4 square inches Find the area By theem 111 the ratio of the areas of a scaled polygon and its iginal equal to the square of the scale fact If you know the area of the iginal polygon and the scale fact of the enlargement, you can find the area of the enlarged polygon by multiplying the iginal area by the scale fact squared B F example, if a triangle has an area of 10 and a similar triangle created by scaling each side of the iginal triangle by, then the area of the new triangle will be the scale fact between Sample answer: If you know the area of the iginal polygon and the scale fact of the enlargement, you can find the area of the enlarged polygon by multiplying the iginal area by the scale fact squared The ratio of their areas 30 the area of of A, AC = 15 inches, PT = 6 inches, and 4 square inches Find the area C D The given triangles are similar, so the sides are proptional AC and PT are cresponding sides, so and The area of D 150 in The crect choice D B C D The given triangles are similar, so the sides are proptional AC and PT are cresponding sides, so and the scale fact between 31 ALGEBRA Which of the following shows facted completely? F (x 18y)(x + 4y) G (x 9y)(x + 4y) H (x 9y)(x + 4y) J (x 1y)(x + 3y) The ratio of their areas The crect choice J J The area of D 150 in The crect choice 3 EXTENDED RESPONSE The measures of two complementary angles are represented by x + Page 1 and16 5x 9 a Write an equation that represents the relationship

17 9 = 61 The crect choice J 11-5 Areas of Similar Figures J 3 EXTENDED RESPONSE The measures of two complementary angles are represented by x + 1 and 5x 9 a Write an equation that represents the relationship between the two angles b Find the degree measure of each angle a If two angles are complementary, then the sum of their angle measure 90 (x + 1) + (5x 9) = 90 a (x + 1) + (5x 9) = 90 b SAT/ACT Which of the following are the values of x f which (x + 5)(x 4) = 10? A 5 and 4 B 5 and 6 C 4 and 5 D 6 and 5 E 6 and 5 (x + 5)(x 4) = 10 Solve f x b If two angles are complementary, then the sum of their angle measure 90 (x + 1) + (5x 9) = 90 Solve f x So, the crect choice E So, the angle measures are (14) + 1 = 9 and 5(14) 9 = 61 a (x + 1) + (5x 9) = 90 b SAT/ACT Which of the following are the values of x f which (x + 5)(x 4) = 10? A 5 and 4 B 5 and 6 C 4 and 5 D 6 and 5 E 6 and 5 E 34 In the figure, square WXYZ inscribed in R Identify the center, a radius, an apothem, and a central angle of the polygon Then find the measure of a central angle (x + 5)(x 4) = 10 Center: point R, radius:, apothem:, central angle:, A square a regular polygon with 4 sides Thus, the measure of each central angle of Solve f x square WXYZ 90 center: point R, radius: angle: YRX, 90, apothem:, central Find the area of the shaded region Round to the nearest tenth esolutions Manual - Powered by Cognero So, the crect choice E Page 17

18 center: point R, radius:, apothem:, central angle: YRX, 90 Find the area of the shaded region Round to the nearest tenth Use the fmula f finding the area of a regular polygon replacing a with OT and P with 3 AB to find the area of the triangle Use the fmula f the area of a circle replacing r with OB 35 The inscribed equilateral triangle can be divided into three congruent osceles triangles with each central angle having a measure of 10 Area of the shaded region = Area of the circle Area of the given triangle Substitute Apothem the height of osceles triangle AOB, so it bects AOB and Thus, and AT = BT Use trigonometric ratios to find the side length and apothem of the regular polygon 663 cm 36 The radius of the circle half the diameter 3 feet The area of the shaded region the difference of the area of the rectangle and the area of the circle Use the fmula f finding the area of a regular polygon replacing a with OT and P with 3 AB to find the area of the triangle Page 18

19 Areas cmof Similar Figures The regular pentagon can be divided into 5 congruent osceles triangles with each central angle having a measure of 7 36 The radius of the circle half the diameter 3 feet The area of the shaded region the difference of the area of the rectangle and the area of the circle Apothem the height of the osceles triangle AOB, so it bects AOB and Thus, and AT = BT Use trigonometric ratios to find the side length and apothem of the polygon Area of the shaded region = Area of the rectangle Area of the circle Substitute Use the fmula f finding the area of a regular polygon replacing a with OT and P with 5 AB 617 ft Use the fmula f the area of a circle replacing r with OB 37 The regular pentagon can be divided into 5 congruent osceles triangles with each central angle having a measure of 7 Area of the shaded region = Area of the circle Area of the pentagon Page 19 Substitute

20 Area of the shaded region = Area of the circle Area of the pentagon Substitute m in Find each measure 38 m 5 By theem 101, if two secants chds intersect in the interi of a circle, then the measure of an angle fmed one half the sum of the measure of the arcs intercepted by the angle and its vertical angle We know that the sum of the arcs intercepted by 6 and its vertical angle will have a measure of 360 ( ) = 85 By theem 101, if two secants chds intersect in the interi of a circle, then the measure of an angle fmed one half the sum of the measure of the arcs intercepted by the angle and its vertical angle Th means that Theem 101 tells us that m 6 half th: m m 6 By theem 101, if two secants chds intersect in the interi of a circle, then the measure of an angle fmed one half the sum of the measure of the arcs intercepted by the angle and its vertical angle We know that the sum of the arcs intercepted by 6 and its vertical angle will have a measure of 360 ( ) = 85 Label the angle that fms a linear pair with as By theem 1013, if a secant and a tangent intersect at the point of tangency, then the measure of each angle fmed one half the measure of its intercepted arc Theem 101 tells us that m 6 half th: Since and are supplementary angles Page 0

21 11-5 Areas of Similar Figures m State whether the figure has plane symmetry, ax symmetry, both, neither 7 Label the angle that fms a linear pair with Consider rotating the cylinder about its vertical ax Any degree of rotation will result in a symmetrical shape Rotating the cylinder about any other ax will not provide symmetry as By theem 1013, if a secant and a tangent intersect at the point of tangency, then the measure of each angle fmed one half the measure of its intercepted arc Since and are supplementary angles State whether the figure has plane symmetry, ax symmetry, both, neither The cylinder has ax symmetric about its vertical ax Now consider a vertical plane that cuts through the cylinder along its ax If the cylinder reflected through th plane, it will be symmetrical If a hizontal plane cuts through the center of the cylinder, then the reflection will again produce symmetry Any other plane, such as a vertical plane cutting through the right side, will not produce symmetry The cylinder has plane symmetry about any vertical plane that cuts in line with the central ax, and also through the hizontal plane that cuts the cylinder in half The cylinder has both ax and plane symmetry Consider rotating the cylinder about its vertical ax Any degree of rotation will result in a symmetrical shape Rotating the cylinder about any other ax will not provide symmetry both 4 YEARBOOKS Tai resized a photograph that was 8 inches by 10 inches so that it would fit in a 4-inch by 4-inch area on a yearbook page a Find the maximum dimensions of the reduced photograph b What the percent of reduction of the length? Page 1 YEARBOOKS Tai resized a photograph that was 8 inches by 10 inches so that it would fit in a 4-inch by

22 100% 40% = 60% The cylinder has both ax and plane symmetry 11-5 Areas of Similar Figures both 4 YEARBOOKS Tai resized a photograph that was 8 inches by 10 inches so that it would fit in a 4-inch by 4-inch area on a yearbook page a Find the maximum dimensions of the reduced photograph b What the percent of reduction of the length? YEARBOOKS Tai resized a photograph that was 8 inches by 10 inches so that it would fit in a 4-inch by 4-inch area on a yearbook page a Find the maximum dimensions of the reduced photograph b What the percent of reduction of the length? a The photograph should be fit in to a 4-inch by 4inch area so no side should exceed 4 in The longest side, 10 in, should be reduced to 4 in Let x be the other dimension of the reduced photograph The scale ratio of cresponding side lengths will be equal: a 3 in by 4 in b 60% Refer to the figure at the right to identify each of the following 43 Name all segments parallel to Two lines are parallel if they are coplanar and do not intersect The only two planes that contain AE are the pentagon ABCDE, and the rectangle AELP If we imagine the lines extending infinitely in each plane, then the only line that does not intersect AE LP 44 Name all planes intersecting plane BCN The planes that intersect plane BCN are ABM, OCN, ABC, LMN The maximum dimensions of the reduced photograph 3 in by 4 in ABM, OCN, ABC, LMN b The side whose length 10 inches should be reduced to 4, which 40% of the iginal length The iginal photo was reduced by 100% 40% = 60% 45 Name all segments skew to a 3 in by 4 in b 60% Two lines are skew if they do not intersect and are not coplanar The following segments meet th criteria: Refer to the figure at the right to identify each of the following 43 Name all segments parallel to Two lines are parallel if they are coplanar and do not intersect The only two planes that contain AE are the pentagon ABCDE, and the rectangle AELP If we imagine the lines extending infinitely in each Page