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6.2 – Use Proportions to Solve Geometry Problems. Complete the statement. y. If. , then. x. Complete the statement. x. If. , then. y. Complete the statement. 9+ y. If. , then. y. Complete the statement. 5+11. If. , then. 11.
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Complete the statement. y If , then x
Complete the statement. x If , then y
Complete the statement. 9+y If , then y
Complete the statement. 5+11 If , then 11
Use the given information and the diagram to find the unknown length. 3x = 2 2 3 x =
Use the given information and the diagram to find the unknown length. 3x = 24 x = 8
Use the given information and the diagram to find the unknown length. 18x = 180 x = 10
Use the given information and the diagram to find the unknown length. 12x = 144 x = 12
Similar Polygons: • Corresponding angles are congruent • Corresponding sides are proportional
Scale Factor: The ratio of the lengths of two corresponding sides of similar figures.
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. Angles A D B E C F Sides:
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. Angles C M D J E K F L Sides:
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor. Sides: Angles A F B D C E
Yes, they are similar. ABC ~ FDE Scale factor:
Sides: Angles Q W No, they are not similar. R X S Y T Z
The polygons are similar as noted. Find the value of x. 6x = 48 x = 8
The polygons are similar as noted. Find the value of x. BCED ~ KLMJ 8x = 144 x = 18
The two triangles are similar. Find the values of the variables. 6m = 66 m = 11
The two triangles are similar. Find the values of the variables. 6m = 66 12n = 48 m = 11 n = 4
5. The two figures are similar. Find the scale factor of their sides. Then find the ratios of their perimeters. What do you notice? 18 12 12 8 6 4 Scale Factor: They are the same! Ratio of Perimeters:
ratio If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths perimeters side
The ratio of one side of a picture to the corresponding side of a larger picture is 2:7. The perimeter of the smaller picture is 16 inches. Find the perimeter of the larger picture. 2x = 112 16 x = 56in x 2 7
7. In the diagram, WXYZ ~ BCDE. • Find the scale factor of WXYZ to BCDE.
7. In the diagram, WXYZ ~ BCDE. b. Find the values of XY and YZ. 4.5 4.5 2XY = 9 XY = 4.5
7. In the diagram, WXYZ ~ BCDE. b. Find the values of XY and YZ. 9 4.5 4.5 2XY = 9 2YZ = 18 XY = 4.5 YZ = 9
7. In the diagram, WXYZ ~ BCDE. c. Find mC. 9 mC = 117° 4.5 4.5
7. In the diagram, WXYZ ~ BCDE. d. Find the perimeter of WXYZ. 9 9 + 4.5 + 4.5 + 6 4.5 4.5 24u
HW Problem 6.3 # 12 60 x x = 36in 3 5