7-1 Ratios and Proportions

The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.

3:5 : 7 3 :5 : 7x x x3 5 7 180x x x

Triangle Angle Sum=180˚15 180x115 155 180x

12x

12

1

3

2

3 36

5 5 60

7 7 812 4

x

x

x

36+60+84 = 180 true

The ratios of the angles in quadrilateral is 2:4:6:3 Find the measure of the angles.

2 : 4 : 6 :3 2 : 4 : 6 :3x x x x2 4 6 3 360x x x x

Quad. Angle Sum=360˚15 360x

115 155 360x

24x

2 2 48

4 4 96

6

24

24

246 144

3 23 724

x

x

x

x

48+96+144 +72= 360 true

The ratios of the side lengths in quadrilateral is 2:3:5:4 and the perimeter is 154 feet. Find the length of the shortest side.2 :3:5 : 4 2 :3 :5 : 4x x x x2 3 5 4 154x x x x

14 154x

114 144 154x

11x

:

2 2 211 2Shortest sidex

22 feet

The ratios of the side lengths in a triangle is

and the perimeter is 31.5 feet. Find the length of the

longest side.1 1 1 1 1 1: : : :4 3 6 4 3 6

x x x

42x

:1 143

4213

longest side

x

14 feet

1 1 1: :4 3 6

1 1 1 31.54 3 6x x x

3 31.54x

3 34 1

1.5x

3 4 31.5x

3 126x

The perimeter of a rectangle is 270 inches. The ratio of its length to width is 7:2 Find the area of the rectangle.72

lw

2 7l w 2 72 2l w

27wl

2 2 270l w Perimeter rule2 2 27072w w

9 270w

30w

307105

2l

A l w 105 30 3150

The perimeter of a rectangle is 77 inches. The ratio of its length to width is 6:5 Find the area of the rectangle.65

lw

5 6l w 5 65 5l w

56wl

2 2 77l w Perimeter rule2 6 75

2 7w w

4.4 77w

17.5w

17.6621

5l

A l w 21(17.5) 367.5

7-2 Similar Polygons

Determine whether the two triangles are similar. If yes, write the similarity statement and the scale factor.

<L=<R<N=<QTherefore, YES similar by AA postulate

StatementLMN~RPQscale factor 5.6 7

4 5

Find LM

2 5.67.5 4x

4 2 7.5 5.6x

4 8 42x 4 34 8.5x x

2 8.5 2 10.5LM x

Find PQ

1 411.9 5.6y

5.6 1 11.9 4y

5.6 5.6 47.6y 5.6 53.2 9.5y y

1 9.5 1 8.5PQ y

Two similar rectangles have a scale factor 3:2 . The perimeter of small rectangle is 50 feet, find the perimeter of large rectangle. 32

L

S

PP

Since 3 greater than 2, so PL is in the top.32 50

LP 2 150LP 75LP

75 feet

Two similar pentagons have a scale factor 3:7 . The perimeter of larger pentagon is 42 feet, find the perimeter of smaller rectangle. 37

S

L

PP

Since 3 smaller than 7, so Ps is in the top.37 42

SP 7 126SP 18SP

18 feet

Polygons are similar. Find x6

3 4x

4 18x4.5x

Polygons are similar. Find y1 48 6y

6 1 32y

4.3x

6 6 32y 6 26y

8 2:12 3

scale factor

P(∆DEF)=30

23

S

L

PP

2 303 LP

2 90 45L LP P

7-3 Similar Triangles

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.80˚

58˚

Yes similar by AA ∆ABC ~ ∆EDF

Determine whether the two triangles are similar. If yes, write the similarity statement and the scale factor.<A=<E<B=<DTherefore, YES similar by AA postulate∆ABC ~ ∆EDC 38.5 7:11 2

scale factor

Find length of AC3 8 72 2

xx

2 3 8 7 2x x 6 16 7 14x x 6 7 14 16x x

2x 2x

3 8 142AC

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. 6 3

4 2

7.5 35 2

9 36 2

Yes similar by SSS postulate. ∆ABC ~ ∆DEC

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.