LESSON 7-1 I can determine whether a dilation is an enlargement, a reduction or congruence transformation I can determine the scale factor for a given dilation

size

image preimage enlargement reduction congruent

reduction 3/6 or 0.5 enlargement 6/4 or 1.5

22 mm 28 mm 22 mm C’ B’ 66 mm 84 mm 66 mm enlargement 3 A’

B’ D’ C’ 1/3 reduction

P’(rx, ry)

(-4, 4) (-2, -6) (6, 6)

(-2, 1.5) (-1, -2) (2.5, -1)

r = image preimage 4 = 6 x x = 1.5

r = image preimage = x 5 x =

240 in 96 in 180 in = = = x 180 x = 3 in

60 in 60 2 = = x 5 x = 150 in

7-1 worksheet ASSIGNMENT

LESSON 7-2 I can write ratios. I can use properties of proportions.

quotient with the same units a : b Write with : or as a fraction, a/b

females : males

elective : non-elective 2 :3

a : b : c Cannot be written as a fraction Ex: ratio of freshmen to sophomores to juniors

5 7 8 x x x 5x + 7x + 8x = x = 240 x =

x x x 2x + 10x + 3x = x = 180 x = 12 24° 120° 36°

7x 3x 7x 3x 20x = 140 x = 7 L W L = 49

fractionsequal diagonals 4(5) = 10(2)

8y =72 y = 9 6x =163.8 x = 27.3

4(2x + 3) = 40 8x + 12 = 40 x = 3.5 3(x – 1) = 4(x + 1) 3x – 3 = 4x + 4 x = -7

length width 40 9 = 16 x 40x = 144 x = inches

miles inches 4 1 = x 3.5 x = miles

gal miles = x 350 x = gallons

wide tall = x 18 x = inches ? 18

7-2 worksheet ASSIGNMENT

LESSON 7-3 I can identify similar figures. I can find missing side lengths in similar figures.

PENTOMINOES

USE 4 TILES TO MAKE THIS SHAPE

DOUBLING Work with your partner to make a shape like the “F” tile, but twice as big Use colored pencils to record your answer on the back of the worksheet Double as many other Pentominoes as you can. Use the grid paper if needed Record all answers using colored pencils

shape size shape size

congruent proportional congruent similar

All = 1.5 Similar,all angles congruent, all sides proportional.

X Y Z All = 2 Similar,all angles congruent, all sides proportional.

13 x = 14 7 x = 6.5

x 9 = 8 12 x = 6 10 y = 8 12 y = 15

Find x first 18 x = x = 27 27

Find y next! y = (y + 1) = y + 18 = y = 15 x = 27, y = 15

11 12 Perimeter = = 33

J K L MN L y 2 x x = 5 2 x = y = 5 2 y = 5

x = 3x (3x + 3) =3(x + 4) 6x + 6 = 3x + 12 x = 2

7-3 worksheet ASSIGNMENT

LESSON 7-4 I can identify similar triangles. I can use similar triangles to solve problems.

SSSSAS ASA AAS HL

similar by SSS~ == Not similar ≠

Not similar ≠≠ Similar by AA~ 30° 60° ΔMKS ~ΔQTR

7-4 worksheet ASSIGNMENT

LESSON 7-5 I can use the Triangle Proportionality Theorem to find parts of triangles I can use the Triangle Midsegment Theorem to find parts of triangles. I can recognize and use proportions to find relationships between altitudes, angle bisectors and medians of similar triangles.

parallel proportional

x 7 6 x = x = 18

12 x 6 7 = x = 14 x 14 NQ = 26

22 x x =x = 12

x – 4 x – = x = 7.5

endpoints midpoints2 sides parallel half

35 2 = 17.5 X =

R S T X Y 12 RS = 2(12) = 24

proportional

6 5 7 x x = x = 8.4

x = x x = 18

x x = x = 3

x 8 x = x = 4

7-5 worksheet ASSIGNMENT

WARM-UP… PLEASE SHOW WORK! Suppose the triangles below are similar. Find x, y and z x y z x = 4y = 7.5 z = 10.5

LESSON 7-6 I can solve problems involving relationships between parts of a right triangle and the altitude (height) to its hypotenuse (longest side).

ΔABC D A C D CB ΔACDΔCBD

2 x x 6 2 x x 6 = = 3.46

3 x y 9 y x 12 3 x x = 9 y y = = 6= 10.39

2 y z 5 z y 7 x x 2 x x 5 = 2 y y 7 = 5 z z 7 = x = 3.16y = 3.74z = 5.92

2 x x 6 = 2 y y 4 = 4 z z 6 = x = 3.46y = 2.83z = 4.90

7-6 worksheet ASSIGNMENT