Download Analytic Geometry Fall Semester Final Review Unit 1 Dilations 1

Analytic Geometry Fall Semester Final Review
Unit 1
Dilations
1. Dilate the figure with a scale factor of ½ and the center at the origin. Then list the location of the
dilated points.
A’ =
B’ =
C’ =
D’ =
Similar Triangles
2. The following triangles are similar. Find the measure of each angle and the measure of each side.
a. mz 
b. mc 
c. AC 
3. In the following diagram, AC II DE. Find the length of side BE.
d. YZ 
List the different theorems that can be used to prove two triangles similar:_____________________
4. Determine if the following triangles can be proven similar. If they can, tell by which theorem.
.
a. _____________________
b. ____________________________
5. A flagpole casts a shadow 12 feet long at the same time that a vertical sign 8 feet tall casts a
shadow 3 feet long. Sketch a picture and then use similar triangles to find the height of the
flagpole.
Properties of Lines and Angles
6. Find the missing angle measures by solving for x.
Congruent Triangles
List the different theorems that can prove two triangles congruent: __________________________
7. Write a two-column proof to prove that ABC  DBC
8. For two triangles, ABC and XYZ , you are given that AB  XY , B  Y , C  Z . Draw
a picture. The two triangles would be congruent by which congruency theorem?
Pythagorean Theorem
9. The diagram below shows three similar right triangles. Find the length of side BD.
Hint – Identify the labeled sides as short leg, long leg, or hypotenuse.
Triangle Midsegment Theorem
10. In the diagram, ST and UT are midsegments. If PQ is 12cm and ST is 5cm, find the length of
UT and PR .
Properties of Quadrilaterals
11. Find the value of x. Then, find the measure of the side.
Geometric Constructions
12. Name the construction that has been created.
a. __________________________________
b. _____________________________________
c. _________________________________
d. _____________________________________
Analytic Geometry Fall Semester Final Review
Unit 2
sin(Θ) = _________
cos(Θ) = ___________
tan(Θ) = ____________
Trigonometric Ratios
In right triangle ABC, C is the right angle, BC  8 and AB  10 .
1. Draw a picture.
2. Find the length of AC .
3. What is sin(A)?
4. Find cos(A).
5. Find tan(B).
Inverse Trig Functions - Finding Angles
6. Find the indicated angle.
7. Find the measure of Θ.
Trig Functions – Finding side lengths
8. Find the length of side x.
9. Find the length of side x.
Angle of Elevation and Depression
10. Ricardo is standing 75 feet from the base of a building. The angle of elevation from the ground
where Ricardo is standing to the top of the building is 320. What is the height of the building?
11. From the top of a barn 25 ft tall you see a cat on the ground. The angle of depression of the cat
from the horizon is 400. How many feet must the cat walk to reach the barn? Draw a picture!
Special Right Triangles: 450 – 450 – 900 and 300 – 600 – 900 triangles
Label the side lengths with the formulas for each special right triangle.
450 – 450 – 900
300 – 600 – 900
12. A 450 – 450 – 900 triangle has legs
of length 6. Find the length of the
hypotenuse. Draw a picture.
13. The altitude of an equilateral triangle
is length 6. Find the hypotenuse.
Analytic Geometry Fall Semester Final Review
Unit 3
Central and Inscribed Angles
Given the circle with center B, CE and DF are diameters and FBG  56 0 .
D
C
B
G
E
F
1. Find the measure of the remaining angle.
2. Find the measure of each arc in the circle.

In the circle below, m a d  46 0
3. Find the measure of arc e.
4. Find the measure of c
5. Find the measure of d
Angles Inside and Outside a Circle:
6. Find the measure of the arc.
7. Find the measure of angle R.
8. Find the measure of angle V.
9. Find the measure of arc TU.
Segment Lengths
10. Find x.
11. Find x.
Arc Length and Sector Area
12. Find the arc length and sector area of the bolded portion of the circle.
13. The diameter of a bike wheel is 12 inches. There are 9 spokes on the wheel. What is the length
between each spoke? What is the area in between each spoke?
Converting Between Degrees and Radian Measures
14. Convert 1200 to radians.
Volume and Surface Area
15. If you triple the length of the radius in a sphere, how does it affect the volume?
16. I candle company makes candles in the shape of a cylinder. Their best-selling candle has a height
of 10 inches and a diameter of 14 inches. How much wax is needed to make one candle?