Geometry
Final Review 2014
Name:_____________________
Period:____ Date: ___________
1. Construct the perpendicular bisector to AB . Label this segment DE . Label the point where DE intersects AB as
point, C. What is true about AC and BC ? How do you know?
2. Describe the process that you used to construct DE . How do you know that DE is perpendicular to AB ?
3. Construct the angle bisector to angle C .
4. Describe the steps you took to construct the angle bisectors.
5. How do you know that the two angles created by the bisector are congruent?
6. If U is the midpoint of FN , find the value of x, the length of UN, and FN.
7. Solve for X and Y in the figure.
(5y)o
85o
(2x – 5)o
8. Using the figure at the right, and the facts
mA0 B  4 x  4
mA0C  10 x  22
mC 0 D  9 x  7
Solve for x and then find
mA0 B 
mB0C 
mC 0 D 
State whether each mapping is a reflection, rotation, translation or a combination of transformations.
9.
ABCD
GHCD
_______________________
10.
HGJI
LMJK
_______________________
11.
GFED
RQOP
_______________________
12.
MNOP
ABCD
_______________________
Draw the image and find the coordinates of the vertices of the image of PQRS for each transformation.
P (-5, 0) Q (-2, -2) R (-3, -4) S (-5, -6)
13. Reflection across
.
14. Translation
P’ ________ Q’ ________ R’ ________ S’ ________
P’ ________ Q’ ________ R’ ________ S’ ________
15. Are the two figures in the diagram congruent? _______
If they are, what rigid motions create the congruence?
Write a rule to describe the rigid motion:
List all pairs of congruent sides and angles:
16. Are the two figures in the diagram congruent? _________
If they are, what rigid motions create the congruence?
Write a rule to describe the rigid motion:
List all pairs of congruent sides and angles:
17. Find the slope of each line and then explain why each set of lines are Parallel, Perpendicular, or Neither. Be sure
to justify your answer using the slopes of the lines.
Slope of A= _______________
Slope of B= _______________
Slope of C= _______________
Lines A and B are:
Lines B and C are :
18. Which point is the closest to the point P(3, 5)? Justify your answer using the distance formula.
A(5, -4) or B(-1, -3)
19. The line segment AB has endpoints, A(2, 3) and B(-4, 9). Using the midpoint formula, find the coordinates of the
midpoint, C.
20. For each parallelogram, solve for x.
x = _____________
x = __________________
21. Figure CFED is a parallelogram. Given that EJ = 3x + 4 and JC = -4 + 5x, find EJ.
EJ = _________________
22. The quadrilateral, EFGH, has the vertices, E(-1, 2), F(0, 4), G(4, 2), and H(3, 0).
Graph the points and draw the quadrilateral.
What type of quadrilateral is it? __________________________
Using properties and showing your work, prove why you think it is this
type of quadrilateral.
D. What is the perimeter of the quadrilateral? _________________
E. What is the area of the quadrilateral? _______________
23. The quadrilateral, ABCD, has the vertices, E(1, 6), F(7, 2), G(3, -4), and H(-3, 0).
Graph the points and draw the quadrilateral.
What type of quadrilateral is it? __________________________
Using properties and showing your work, prove why you think it is this
type of quadrilateral.
D. What is the perimeter of the quadrilateral? _________________
E. What is the area of the quadrilateral? _______________
24. State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot
be proved congruent, write not possible.
_________________
_________________
_________________
________________
_________________
_________________
25. J is the midpoint of GH . GK is parallel to LH . Which congruence criterion can be used to prove
GJK  HJL ? (multiple choice)
ASA
SAS
SSA
SSS
26. PN  QN , and MN bisects PNQ . Which congruence criterion can be used to prove MPN  MQN ?
(multiple choice)
ASA
SAS
SSA
SSS
27.
28. Given: X is the midpoint of
Prove: AXB  DXC
and
Statements
29. Given:
Prove:
Reasons
, D is the midpoint of
Statements
Reasons
30. To find the distance AB across a pond, you locate points as follows.
Starting at A and walking along a straight path, you walk 46 feet and put a marker at C. Then you walk 46 feet
farther and put a marker at D. Starting at B, you walk to C, measuring the distance you walked to be 58 feet. Then
you walk 58 feet farther and put a marker at E. Finally, you measure the distance from D to E, as shown. Explain
how to use this information to find AB.
31. Consider the geometric construction below of an angle bisector.
Using congruent triangles prove that BX is the bisector of ABC .
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
32. Solve each proportion for x.
x = _____________
x = _____________
33. For each set of triangles below a) write the similarity statement IF they are similar, and b) name the postulate or
theorem that you can use to prove they are similar. If the triangles are not similar, write not similar.
∆ABC~∆______________________
_∆PXM~ ∆______________________
_∆ABC~ ∆____________________
34. Find the value of x for each set of similar triangles.
-2
x = _____________
x = _____________
35. To find the distance XY across a lake, you use the points shown in the figure. Explain how to use this information
to find XY. Show all your work.
36. Find the value of x for the figure
x = _____________
37. A hippo 6 ft tall casts a shadow 8 ft long. At the same time, a giraffe casts a shadow 21 ft long.
How tall is the giraffe? Draw a picture representing the situation and solve.
38. Find the value of the variable(s). Write all answers in Simplest Radical Form.
x = __________________
x = ________________
y = ________________
z = _______________
39. Find the coordinates of each vertex if the image is dilated by a scale factor of 2.5 using the origin as the center of
dilation. (HS.G.CO.2 & HS.G.SRT.1)
A: ______________
A
B: ______________
C: ______________
Complete the rule, (x, y)→______________
40. What is the scale factor for the dilations shown in the figure?
Describe the transformations you could use to map figure
ABC to DEF.
41.
C
B
42. Find the value of each variable. Leave your answers in simplest radical form.
x = _________
z = _________
c = _________
y = _________
10
x = _________
a = _________
a = _________
y = _________
b = _________
b = _________
43. Write the ratios for sin P, cos P, and tan P.
sin (P) =
cos (P) =
tan (P) =
There is a way to find sin(P) using its compliment, angle Q. Explain how this can be done.
____________________________________________________________________________________
____________________________________________________________________________________
44. Find the value of x. Round side lengths to the nearest tenth and angle measures to the nearest degree.
10
24o
x = _________
x = _________
x = _________
45. Find the value of x. Round side lengths to the nearest tenth and angle measures to the nearest degree.
x = _________
x = _________
x = _________
46. A forest ranger looking out from a ranger’s station can see a forest fire at a 28o angle of depression. The ranger’s
position is 60 m above the ground. Find the direct distance from the ranger’s position in the ranger’s station to the
fire. Use the diagram below.
47. A person standing 30 ft from a flagpole can see the top of the pole at a 40o angle of elevation. The person’s eye
level is 5 ft from the ground. Draw and label a diagram then find the height of the flagpole.
48. Find the surface area and volume of each figure.
Surface Area=
Volume=
Surface Area=
Volume=
Surface Area=
Volume=
Surface Area=
Volume=
49. A block of wood 9 feet high has solid columns cut out of it, each with radius 2 feet.
a. What is the volume of the block of wood before the columns are cut out?
b. What is the volume of each cylinder?
c. What is the volume of the left over wood?
50. Find the volume and surface area of the composite figure at right.
51. Find the Surface area and volume of the paint-roller.
52. Find the volume of the sphere.
V = ____________________
53. Find the Surface Area of the sphere.
SA = _______________
54. What is the arc length of
55. Find the area of the shaded sector.
Arc Length = ___________
Find each indicated measure for
Area = ___________
.
56.
_____________ 57.
_____________
58.
_____________59.
_____________
60.
_____________
61. Find the value x and the measure of each missing angle.
x = ______________
62. Using the figure, name each pair of angles:
a and c: ____________
a and b: ____________
b and e: ____________
d and e: ____________
x = ______________
measure of acute angle = ___________
measure of obtuse angle = ___________