Name ____________________________________________ Date _______________ Period _______
Geometry Semester 1 Final Review
1. Which type of reasoning is based on patterns you observe?
Inductive Reasoning
2. How would you symbolically represent a line with points A and B on it?
↔
𝐴𝐵
3. What is a two column proof?
A two-column proof shows statements and reasons or justifications for each statement of a proof
aligned in two columns
4. Which statement does not have a true contrapositive?
a. If a polygon is a square, then it is a quadrilateral.
b. If a vehicle is a car, then it has an engine.
c. If a polygon is a quadrilateral, then it is a rectangle.
d. If today is Tuesday, then tomorrow is Wednesday.
5. Write a conditional statement about the Venn diagram below?
If it is a poodle, then it is a dog
6. Use the law of detachment to make a conclusion given the following information:
If two lines intersect at a 90 degree angle, then they are perpendicular.
Line j and line m intersect at a 90 degree angle
Line j and line m are perpendicular
7. Fill in the proof below:
3x+5=14
Subtraction property of equality
8. Which statement’s inverse is true?
a. If an angle’s measure in 120 degrees, then the angle is obtuse.
b. If two angles are vertical angles, then they are congruent.
c. If two angles are complementary, then they are acute.
d. If and angle is bisected, then it is divided into two congruent angles.
9. What are the three undefined terms and what are their corresponding symbols?
Point, Line and Plane
10. What conjectures can be made if line DE and line HK are skew?
DE and HK are noncoplanar
11. Identify the theorem and fill in the blank of the conditional statement below:
If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are
Parallel by the converse of alternate exterior angles Theorem.
12. Using only the given diagram, answer the following questions. Do we know that angles 1 and 5 are
congruent? Why or why not? Are the alternate interior angles congruent? Why or why not?
We do not know that angles 1 and 5 are congruent because we don’t know if lines b and c are parallel or not. We
also don’t know if the alternate interior angles are congruent because we don’t know that the lines are parallel.
13. What postulate would you use to discuss the relationship between angles 1 and 7:
Alternate Exterior Angles Postulate
14. Both figures were attempts to construct congruent segments. Which figure correctly shows a pair of
congruent segments? How do you know this?
Figure 1
Figure 2
Circle A
Figure 1
15. Which construction requires drawing only one arc with a compass?
Constructing Congruent Segments
16. In the diagram below, transversal s cuts across parallel lines q and r. What are Angle 1 and angle 2?
Alternate Exterior Angles
17. Given: n|| m
Prove: ∠1 and ∠3 are supplementary
Complete the proof below by filling in the missing information
Statement
n|| m
∠1 ≅ ∠2
∠2 and ∠3 form a linear pair
m∠2 + m∠3 = 180°
m∠1 + m∠3 = 180°
b.
Reason
Given
Corresponding Angles are congruent
Definition of Linear Pair
a.
Linear Pair Postulate
Substitution
Definition of supplementary
18. Use the diagram to write all statements that would prove that g//h.
Angle 2 and 6 are congruent, Angle 2 and 7 are congruent, Angle 3 and 6 are congruent, Angle 2 +
Angle 8=180
19. Using only the markings shown, what conjecture can be made from the construction?
I.
II.
III.
1  4
m1 + m3 = 180˚
l || k
All 3
20. FGH is an equilateral triangle. What is the perimeter of quadrilateral FGJH ?
96 units
21. Lee constructed AB perpendicular to CD with a compass and straightedge. Macy constructed the angle
bisector, EF , with the same tools. What conjecture can be made?
mCEF  45, mFEB  45
CD  AB
AE  EB
22. Perpendicular bisectors were created using 3 different methods, which ones are correct?
All 3
Method
Diagram
I
II
III
23. Alfonso is using the segment addition postulate to construct a segment that satisfies the equation
AC  2 AB . What should Alfonso do next?
Without adjusting the compass, place the compass tip at point B ' .
24. Which construction only needs three arcs to construct?
Angle Bisector
25. Construct an angle bisector.
26. Define circumcenter and its properties:
The point of concurrency of the perpendicular bisectors of the triangle.
27. Given that ∠1 𝑎𝑛𝑑 ∠2 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑖𝑚𝑒𝑛𝑡𝑎𝑟𝑦 and ∠3 𝑎𝑛𝑑 ∠2 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑖𝑚𝑒𝑛𝑡𝑎𝑟𝑦
Which of the following would you use to prove that ∠1 ≅ ∠3?
I.
II.
III.
Transitive Property of Equality
Angle Addition Postulate
Definition of Complimentary Angles
28. In order to write a proof, which of the following would you use?
Given: Point T is the midpoint of
Prove: PT=RT=ST=QT
Angle Addition Postulate
Segment Addition Postulate
Definition of a Midpoint
Transitive Property
and
and PQ=RS
29. Given 𝑚∠𝑀𝑅𝑇 = 133, solve for g.
24
30. What is the distance between P(-4,3) and Q(6,1)? Round to the nearest tenth.
10.2
̅̅̅̅ is E(-1,0). One endpoint is C(5,2). What are the coordinates of point D, the other
31. The midpoint of𝐶𝐷
endpoint?
(-7,-2)
32. Bricksburg wants to construct a road parallel to the existing railroad. The railroad passes through the
County Train Depot and Trading Post. The new road needs to pass through downtown.
What is the equation of the new road?
2
y   x  12
3
33. ∆𝑅𝑆𝑇 ℎ𝑎𝑠 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠 𝑅(−4, 5), 𝑆(−2, 3), 𝑎𝑛𝑑 𝑇(−5, 2). 𝐼𝑓 ∆𝑅𝑆𝑇 𝑖𝑠 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑡ℎ𝑒 𝑥 −
𝑎𝑥𝑖𝑠 𝑎𝑛𝑑 𝑡ℎ𝑒𝑛 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑒𝑑 2 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛 𝑡𝑜 𝑏𝑒𝑐𝑜𝑚𝑒 ∆𝑅 ′ 𝑆 ′ 𝑇 ′ , 𝑤ℎ𝑎𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 𝑜𝑓 𝑆 ′ ?
(-2, -5)
34. Hexagon ABCDEF has been transformed.
Which transformation would result in the image provided?
Rotation of 180 degrees
35. ∆𝐾𝐿𝑃 has vertices 𝐾(−4, 2), 𝐿(2, 6), 𝑎𝑛𝑑 𝑃(4, −6). It is dilated to form ∆𝐾′𝐿′𝑃′ with the origin as the
center of dilation.
If the coordinates of K’ are (-6, 3), what scale factor was used to form ∆𝐾 ′ 𝐿′ 𝑃′ ?
3/2
36. Endpoints of MN are M (-6,-4) and N (12,8). Points P and Q are collinear with M and 𝑁. If
1
1
MP  MN and MQ  MN , what are the endpoints of PQ ?
3
2
(0,0) and (3,2)
37. A circle with a center at (1,3) and radius of 4 is graphed below.
Write the equation for the circle after it has been translated
right 4 and down 2?
( x  5) 2  ( y  1) 2  16
38. Find the center and radius for the given equation of a circle and then graph it.
( x  4) 2  ( y  2) 2  36 ?
Center: (-4,2)
Radius: 6
39. Given points P(-3, -2) and Q(2, 3) on line m and points R(10, -1) and S(1, -6) on line k, tell whether the
lines are parallel, perpendicular, or neither and explain your reasoning.
Neither, the slopes are not the same and they are not opposite reciprocals
40. Which of the following transformations would create a triangle which is not congruent to ABC?
Translation, Rotation, Dilation, Reflection
41.
N=3, enlargement
42. Similar polygons have corresponding angles that are congruent and
corresponding sides that are Proportional.
43.
44. Find the value of x, given that the triangles below are similar.
A
D
5x
5
E x F
B
4
C
x=2
45. What is the geometric mean of 5 and 15? Write your answer in simplest radical form.
5√3
46. Are the two triangles similar? How do you know?
D
53°
G
60°
60°
C
E
F
67°
H
Yes, by AA
47. Are the two triangles similar? How do you know?
J
H
39 °
M
39 º
K
G
Yes, by AA
48. What is the value of x, given that
?
A
8
P
x
B
12
Q
18
C
12
49. What is the value of x? Write your answer in simplest radical form.
2√3