Download fall review questions

GEOMETRY FINAL REVIEW I FALL 2016
Name
Period
O
E
1. Which points are collinear? Which points are coplanar?

G
C
2. Name the intersection of planes TUCO and TURG.
O
U
B
A
7x – 3

A
4. If M is the midpoint of AC , find x.
C
T

M
Y
T
E
N
R
3. What ray is opposite CA ?
R

G
D

M
4x + 8

C
M
5. If AH bisects MAT , find x.
2x + 14
H
6x – 30
A
T

6.  ABC and  CBD are supplementary angles, m  ABC = 4x +10, and m  CBD = 6x + 20.
Solve for x. What is m  ABC?
7. The endpoints of AB are A(8, ‒2) and B(–8, 12). Find the midpoint of AB .
8. What is the distance between A(‒5, 4) and B(1, ‒4)?
9. What is the circumference of the circle with radius 4.1? Leave your answer in terms of  .
10. All angles in the given figure are right angles. What is the area of the figure?
11. What is the next term of this sequence?
5, 8, 11, 14, 17, 20 ...
12. What is the converse of the given statement?
If Teresa fails her vision test, then she will order glasses.
13. What is the contrapositive of the given statement?
If Vanessa finds a job, then she will go on a shopping spree.
14. Conditional: If a triangle is equilateral, then the triangle has three congruent sides.
Write as a true biconditional.
GEOMETRY FINAL REVIEW I FALL 2016
Name
Period
15. Write a valid conclusion, assuming the following statements are true.
If a polygon is a regular hexagon, then the polygon has exactly six congruent sides.
The polygon is a regular hexagon.
16. Using the transitive property of equality, if mA  mB and mB  mC, then
?
17. Name the property of equality that justifies the statement: mD  mD .
18. E and F are complementary. If mE  2x 10 and mF  3x  20 , what is the value of x ?
19. T and  R are vertical angles. mT  3x  36 & mR  6x – 9 . Solve for x. What is the measure of T ?
20. In the figure, if m3  41 , and 1  3 , what is m2 ?
For Questions 21-22, refer to the figure below.
21. Identify the plane parallel to plane HIGF.
̅̅̅̅?
22. Identify four segments which are skew to 𝐺𝐾
For Questions 23-25, refer to the figure at the right.
23. Identify the special name for each angle pair :
∠ 4 and ∠ 8
∠ 2 and ∠ 7
∠ 3 and ∠ 5
∠ 4 and ∠ 5
24. Given a ║ b and m∠ 2 = 61°, find m∠ 6.
25. Given a ║ b, m∠ 4 = 5x + 100, and m∠ 6 = 7x + 20, find the value of x.
26. Find the slope of the line that contains (–4, 3) and (10, 5).
1
27. Write an equation of the line with slope 3 that contains (4, – 8) in point slope form.
GEOMETRY FINAL REVIEW I FALL 2016
Name
Period
28. Write an equation of the line containing (2, –3) and (6, 17) in slope intercept form.
29. Given the figures, describe each triangle
a) by angles and b) by sides
30. Solve for x, y and z.
31. Complete the proof.
Given: L is the midpoint of ̅̅̅̅
𝐽𝑀, ̅̅̅
𝐽𝐾 ∥ ̅̅̅̅̅
𝑁𝑀
Prove: △JKL ≅ △MNL
Statements
Reasons
1. Given
2. __________________________
3. Given
4. __________________________
5.___________________________
6.___________________________
̅̅̅̅̅.
1. L is the midpoint of 𝐽𝑀
̅ ≅ ̅̅̅̅
2. 𝐽𝐿
𝑀𝐿
̅̅̅
̅̅̅̅̅
3. 𝐽𝐾 ∥ 𝑁𝑀
4. ∠ 2 ≅ ∠ 4
5. ∠ 1 ≅ ∠ 3
6. △JKL ≅ △MNL
4
3
1
2
10
5
x  4 and y  x  11 ,
8
4
are these lines parallel, perpendicular or neither?
32. Given the equations of the lines y 
33. If ABC  XYZ , then BC = ____.
34. Can the two triangles be proved congruent? If so, by which method?
35. Complete the proof.
Given:  E   A , AC = EC
Prove: C is the midpoint of BD
Statements
Reasons
D
1
2 C
E
GEOMETRY FINAL REVIEW I FALL 2016
1.)
2.)
1  2
3.)
∆ABC  ∆EDC
Name
Period
1.)
2.)
3.)
4.)
4.)
36. 5.)
Find the value of x.
x
5.)
20°
37. Find the value of x.
2x - 10
20
22
D
38. Find the value of x.
8x – 10
2x + 14
A
39. Find the value of x.
C
B
7
x
40. Z is the centroid of  ABC. If CZ = 8, what is ZX?
41. What is the best description of AB for each triangle?
42. What is the best description of B and P?
43. What is the first step of the following indirect proof?
Given: The side lengths of a triangle are 4, 4, and 6.
Prove: The triangle is not a right triangle.
44. Could the following lengths be the sides of a triangle?
3, 4, 6
6, 7, 13
7, 9, 17
45. Lists the angles in order from the smallest to the largest.
46. What are the possible lengths for x, the third side of a triangle, if two sides are 5 and 11?
GEOMETRY FINAL REVIEW I FALL 2016
Name
Period
47. Write an inequality relating LP and XA.
48. What is the sum of the interior angle measures of a regular pentagon?
49. What is the measure of one interior angle of a regular 15-gon?
50. If the exterior angle of a regular polygon is 15°, how many sides does the polygon have?
51. Solve for s in this parallelogram. What is mÐ1?
1
52. For what value of x must ABCD be a parallelogram?
53. How can you prove that a quadrilateral is a rhombus?
54. ABCD is a rectangle. If AC = 6x + 2 and BD = x + 22, find the value of x.
55. In the isosceles trapezoid at the right, what is the measure of 1, 2, and 3?
56. For this rhombus, what is the measure of 1, 2, 3 and 4?
57. Given the kite, find the measure of 1 and 2.
58. Sketch the construction of the bisector of A.
A
GEOMETRY FINAL REVIEW I FALL 2016
Name
Period
59. Sketch the construction of the perpendicular bisector of BC
B
C
·
60. Sketch the construction of a line perpendicular to k through P.
k
61. Sketch the construction of a line perpendicular to m through R.
m
R
·
P