SOH CAH TOA

SOHCAH TOA

Triangle Similarit

y Postulat

es

Dilations

Special Right Triangl

es

Similar

Figures

Trig Word Problems

Odds &

Ends

1 1 1 1 1 1

2 2 2 2 2 2 2

3 3 3 3 3 3 3

4 4 4 4 4 4 4

1

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Are these two triangles similar? If they are, identify the reason.

Red Question 1

Not enough information (SSA).

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Which statement is true for the triangles below?

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Click here for the answer.Red Question 3

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B) AB and DE are proportional

In similar figures, the angles are congruent, but the sides are proportional. The figures

themselves are similar.

Why are these triangles similar?

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SAS~

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How many times has segment XY been dilated ?

Orange Question 1

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THREE (3)Do not count the original,

or point P, which is the center of dilation.

Orange Answer 1

Which of these statements is true?a) B’ is the center of dilation.b) ABC has been dilated by a factor or 5.c) O is the center of dilation.d) The triangles are congruent.

Click here for the answer.Orange Question 2

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C--O is the center of dilation

Orange Answer 2

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Why do these dilated figures overlap?

Orange Question 3

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One of the vertices (or corners) of the pre-image was used as the center of dilation.

Orange Answer 3

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Which point below is the center of dilation?

Orange Question 4

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point P

Orange Answer 4

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Find x and y in the triangle below.

Yellow Question 1

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Click here for the answer.Yellow Question 2

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Area = ½ b h = ½ (41)(6)

= 123 in²

Yellow Answer 2

Find x and y.

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What is NEVER a reason that two triangles are similar?A) SAS~B) SSS~C) AA~D) SSA~

Yellow Question 4

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What is NEVER a reason that two triangles are similar?A) SAS~B) SSS~C) AA~

D) SSA~ bass-ackwards

Click here for the answer.Green Question 1

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BIt has the same cross products as

the original: zw = xy

Green Answer 1

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The triangles below are similar. The sides marked “20” and “x” are

medians. Solve for x.

Green Question 2

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36x = 360x = 10

Green Answer 2

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On a sunny day, a 12 inch ruler is held perpendicular to the ground. It casts a 30 inch shadow. At the same time, a bush casts a shadow that is

80 inches long. How tall is the bush?

Green Question 3

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30 x = 960x = 32 inches

Green Answer 3

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How wide is the river below (EN)?

Green Question 4

30x = 1800x = 60 ft

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In a right triangle, sinX = 9/15.cosX = 12/15. What is tanX = ?

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tanX = opp/adj = 9/12

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If sinM = 8/17 then tan M = ?

Blue Question 2

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tanM = 8/15

Blue Answer 2

Find a and b.

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sin 71 = 13/bb = 13/sin 71b = 13.7

tan71 = 13/aa = 13/tan 71a = 4.5

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A cat is stuck in a tree. Bill gets a ladder to get him down. The ladder is

8 ft. long. The ladder makes an 80 degree angle with the ground. How

high above the ground does the ladder touch the tree?

Blue Question 4

sin 80 = x/8x = 8sin80x = 7.9 ft.

Click here to return to the game board.Blue Answer 4

A surveyor is 100 feet from a tower. The surveyor’s instrument is 4 feet

above the ground. When the surveyor sights the top of the tower

with his instrument, the angle of elevation is 34°. How tall is the

tower?

Click here for the answer.Purple Question 1

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tan 34 = x/100x = 100 tan 34

x = 67.5tower = 67.5 + 4 = 71.5 feet

Purple Answer 1

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The ladder to a slide is 6 ft. tall. The slide is 11 ft. long. What angle does

the ladder make with the ground?

Purple Question 2

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sin x = 6/11x = sin -1 (6/11)

x = 33.1°

Purple Answer 2

From a point 68 feet from a building, the angle of elevation to a floor on the building is 53 degrees. How many feet high is that floor?

Click here for the answer.Purple Question 3

tan 53 = x/68x = 68 tan 53x = 90.2 feet

Click here to return to the game board.Purple Answer 3

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Mrs. Gasper was practicing her karate and chopped a flag pole. The pole breaks 6 ft.

above the ground. The broken piece forms a 57° angle with the ground. How tall was the

pole before Mrs. Gasper chopped it?

Purple Question 4

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Bill has two pieces of lumber, one is 9 ft. long and the other is 12 ft. long. How

long should a third piece of lumber be in order for Bill to have a right triangle?

Click here for the answer.Pink Question 1

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Use the Pythagorean Theorem:9² + 12² = c²81 + 144 = c²

225 = c²

c = 15 ft

Pink Answer 1

What is the slope of this line?

10 y - 5x = 30

Click here for the answer.Pink Question 2

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10 y - 5x = 30 + 5x + 5x

10 y = 5x + 30 10 10 10

y = ½ x + 3

The slope is ½ .

Pink Answer 2

A park is being built in a city at the intersection of two streets. The park will be shaped like a right triangle. If the park will be 30 meters along Main

Street and 40 meters along First Avenue, how long will the third side

(or hypotenuse) of the park be?

Click here for the answer.Pink Question 3

30² + 40² = (3rd side)²900 + 1600 = c²

2500 = c²cm = 50 meters

Click here to return to the game board.Pink Answer 3

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Find x and y.

Pink Question 4

x + 110 = 180x = 70

3y + 3 = 183y = 15y = 5

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