Geometry Final Review

Dilations & Scale Factor

100

What is Scale Factor?

The number multiplied to a pre-image points to create a smaller or larger similar shape. 

200

Suppose A = (1,2) and the Scale Factor equals 4. What is A'?

A^'=(4, 8)

300

B = (20,-4) and B^'= (-10,2). What is the Scale Factor?

Scale Factor = -1/2

400

Solve for x. 

12/9 = x/20

x = 26.6

500

A = (2,3) B = (8,10) and C = (-1,4). Also, A'= (1,1.5) B'=(4,5) and C'= (-1,2). What is the scale factor?

Impossible. Point C did not have the same scale factor of A and B to create a similar triangle. 

Triangle Similarity

100

What does SAS stand for?

Side-Angle-Side

200

What are the three similarity theorems to prove two triangles are similar?

SAS, SSS, AA

300

What do all sides of similar triangles need to be for them to be similar?

All sides need to be proportionate/have the same scale factor. 

400

Triangle ABC has angle A = 30, angle B = 60. Triangle DEF has angle D = 30 and angle F = 90. 

Are the two triangles similar? Which Triangle Similarity Theorem do we use to prove they are similar?

Yes, by AA.

500

Assume you have two triangles ABC and DEF. On these two triangles, two sets of corresponding sides are proportionate to one another. What additional information is needed to prove that two triangles are similar using SSS? 

Another set of corresponding proportionate sides. 

Special Right Triangles

100

What are the two special right triangles we have done in class?

45-45-90 & 30-60-90

200

Assume we have a 45-45-90 triangle and one of the legs has a length of 6. How long is the hypotenuse?

6sqrt(2)

300

Assume we have a 30-60-90 triangle and let the long leg be a length of 9sqrt(3). What is the length of the hypotenuse?

18

400

Assume we have a 45 -45-90 triangle. Let the hypotenuse by a length of 4. What is the length of the two legs?

2sqrt(2)

500

Assume we have a 30-60-90 triangle. Let the hypotenuse be a length of 8sqrt(3). What is the length of the short leg?

4sqrt(3)

Trig Ratios

100

What is the special word to remember all of our trig ratios?

SOHCAHTOA

200

Let Theta = 58 degrees and the side opposite of it equal 6. What is the length of the hypotenuse?

7.1

300

Let the hypotenuse equal 8 and the side adjacent to theta equal 6.5. What is the measure of Theta?

35.7

400

Let Triangle ABC have angle B equal 90 and angle C equal 45. Let AC = 4sqrt(2). What is the length of AB?

4

500

What function do we need to do to solve for Theta when given the side opposite and adjacent to the angle?

Inverse Tangent

Trig Applications

100

What is the difference between an angle of elevation and angle of depression?

An angle of elevation is looking from the ground up and an angle of depression is looking from the sky down to the ground. 

200

A turtle is looking up to the top of a tree at an angle of elevation of 68 degrees. The turtle is 40 feet away from the tree. How tall is the tree?

99 ft. 

300

An airplane is 13,000 feet in the air and the pilot looks down at a football stadium at an angle of depression of 28 degrees. How far away is the stadium from the pilot?

27690 ft. 

400

A 6ft. man is 40 feet away from the base of a flag pole that is 55 feet tall. What angle of elevation is the man looking up at to see the top of the flag pole?

Angle of Elevation = 50.77 degrees

500

What is Mr. Taylor's wife's name?

Ella