Geometry
1st Semester Final Exam REVIEW
Name________________________
Date_______________Period ____
Chapter 1:
1. Find the next two terms in each sequence.
a) 12, 14, 18, 24, 32, _____, _____
b) 17, 23, 29, 35, _____, _____
2. Use the diagram at the right and circle the word that best completes each sentence.
a) Points A, B, and D are (collinear, noncollinear).
b) Points E, D, C, and B are (coplanar, noncoplanar).
c) Another name for plane Q is (BCD, EFD, AEF).
3. Given the points P(12, -12) and Q(5, 12):
a) Find the distance PQ.
b) Find the midpoint of PQ.
4. Find the perimeter and the area of the figure. All angles in the figure are right angles.
Perimeter ________________
Area ____________________
5. Find the circumference and the area of the circle. Leave your answers in terms of π.
Circumference _____________
Area _____________________
Chapter 2:
6. For the following conditional statement: If two angles are vertical angles, then they are congruent.
a) Write the converse.
b) Determine the truth value of both the statement and the converse.
7. What conclusion can you draw from the following two statements? Circle the best answer.
If you have a job, then you have an income.
If you have an income, then you must pay taxes.
A.
B.
C.
D.
If you have a job, then you must pay taxes.
If you don’t have a job, then you don’t pay taxes.
If you pay taxes, then you have a job.
If you have a job, then you don’t have to pay taxes.
8. Which statement is a good definition? Circle the best definition.
A.
B.
C.
D.
Skew lines are lines that do not intersect.
Parallel lines are lines that do not intersect.
A square is a rectangle with four congruent sides.
Right angles are angles formed by two intersecting lines.
9. Find the value of the variables.
10. Find the value of the variable x.
11.
Chapter 3:
12. Use the diagram at right and the terms alternate interior angles, same-side interior angles,
corresponding angles and vertical angles to best describe each of the following pairs of angles.
a)
b)
c)
d)
e)
f)
13 and 16________________________
2 and 14_________________________
3 and 5__________________________
8 and 14_________________________
7 and 15_________________________
12 and 16 ________________________
13. Find the value of x for which a // t.
14. Find the value of the variable m and classify the triangle by its sides and its angles.
m = ________
Classify by sides_____________________
Classify by angles____________________
15. Find the missing angles.
a.
b.
16. Find the value of the missing angle measures.
a.
b.
17. Find the slope of the line that contains the points A(-2, 3) and B(1, -1).
18. Write an equation for the line that contains point P(-3, 5) with a slope of -1.
19. Are the lines parallel, perpendicular, or neither? Explain your solution.
 x  y  1
2x  3y  6
a.
b.
4 x  6 y  24
y  x7
20. Supply the reason for each step in the proof.
Given: l // m and 4  2
Prove: n // p
Statements:
1. l // m
2. 1  2
3. 4  2
4. 1  4
5. n // p
Reasons:
1.
2.
3.
4.
5.
Chapter 4:
21. 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.
a)
b)
c)
d)
e)
f)
.
22. Draw a picture to represent ΔDEF  ΔGHI. Name all of the pairs of corresponding
congruent parts.
Picture:
Corresponding Sides:
Corresponding Angles:
23. An isosceles triangle has a 52° angle exactly opposite of one of its congruent sides. What are
the measures of all three angles?
24. Complete the two-column proof.
Given: QK  QA, QB bisects  KQA
Prove: KB  AB
Statements:
1. QK  QA
2. QB bisects  KQA
3.  KQB   AQB
4. QB  QB
5. ΔKBQ  ΔABQ
6. KB  AB
Reasons:
1. ________________________________________
2. ________________________________________
3. ________________________________________
4. ________________________________________
5. ________________________________________
6. ________________________________________
Chapter 5:
25. Find x and y, as well as the missing distances.
26. Find x and the missing angle.
90° 5
13
x
y
5y - 36
2x + 1
5
4x -17
27. List the sides of the triangle in order
from shortest to longest.
28. List the angles of the triangle in order from
largest to smallest.
29. Can a triangle have sides with the
given lengths? Explain.
30. Find the value of x.
a) 11m, 12m, and 13m
b) 1.2cm, 2.6cm, and 4.9cm
31. Use angle bisector, perpendicular bisector, altitude,
and/or median to name each type of segment or ray.
DE
AF
DB
CH
________________________
________________________
________________________
________________________
32. Given that Point C is a centroid, find the missing distances.
NC __________
PQ __________
RM __________
PC ___________
M
N
P
C
18
14
6
Q
Chapter 6:
33. Find x., then the lengths of the sides.
R
34. Find x.
a.
S
b.
35. Find the measure of the numbered angles of these parallelograms.
a.
b.
36. Find the values of x and y for which the figure must be a parallelogram.
a.
b.
37. For each parallelogram, (a) choose the best name, and then (b) find the measures of the
numbered angles.
a.
b.
38. The diagonals of a quadrilateral are perpendicular bisectors of each other. Circle the name
that best describes the quadrilateral.
A. rectangle
B. parallelogram
C. quadrilateral
D. rhombus