Download Practice Exam I True / False Indicate whether the statement is true or false. 1. Where 

Name: Class: Date: Practice Exam I
True / False
Indicate whether the statement is true or false.
1. Where a. True
b. False
and , it follows that .
2. The relation between lines, “is perpendicular to,” has a transitive property.
a. True
b. False
3. Where x is the measure of an angle and 0° < x < 90°, the angle is an obtuse angle.
a. True
b. False
4. If and a. True
b. False
5. With a. True
b. False
are complementary, then each of these angles 1 and 2 is acute.
and point G in the interior of , and are complementary.
6. The statement, “If 2 parallel lines are cut by a transversal, then corresponding angles are congruent” can be used to
prove that 2 lines are parallel.
a. True
b. False
7. If two lines in space do not meet, they must be parallel.
a. True
b. False
8. The indirect proof of the statement, “If is not perpendicular to , then ∠1 and ∠2 are not complementary”
begins with the statement, “Suppose that ∠1 and ∠2 are complementary.”
a. True
b. False
Copyright Cengage Learning. Powered by Cognero.
Page 1
Name: Class: Date: Practice Exam I
9. If coplanar lines r and s are cut by transversal t so that alternate exterior angles
are congruent, then r || s.
a. True
b. False
10. It is possible for a triangle to be both isosceles and obtuse.
a. True
b. False
11. The polygon shown is concave.
a. True
b. False
Copyright Cengage Learning. Powered by Cognero.
Page 2
Name: Class: Date: Practice Exam I
Multiple Choice
Indicate the answer choice that best completes the statement or answers the question.
12. Consider the definition: An isosceles triangle is a triangle that has two congruent sides. Which result must follow from
the definition?
a. If is isosceles, then it has two congruent angles.
b. If in , then is an isosceles triangle.
c. If has two congruent sides, then has two congruent angles.
d. None of These
13. In geometry, what is a postulate?
a. statement that defines a term
c. a type of geometric figure
14. If M is the midpoint of b. statement that must be proved
d. None of These
, then it can be proved that:
a. N is also the midpoint of c. .
b. d. None of These
15. When two parallel lines are cut by a transversal, and and , find x.
a. x = 5
b. x = 6
c. x = 7
d. x = 8
are a pair of alternate interior angles formed. If 16. Assuming that statements (1) and (2) are true, which conclusion completes the Law of Negative Inference?
(1) P Q
(2) ∼ Q
a. Q
b. ∼Q
c. P
d. ∼P
17. In a. 20°
c. 60°
, b. 40°
d. 80°
, , and . find .
18. What type of polygon has exactly 8 sides?
a. pentagon
b. hexagon
c. octagon
d. decagon
Copyright Cengage Learning. Powered by Cognero.
Page 3
Name: Class: Date: Practice Exam I
19. For the triangle shown, what is the image of the reflection of the given triangle across a. a right triangle
b. an acute triangle
c. an obtuse triangle
d. an isosceles triangle
?
Completion
Enter the appropriate word(s) to complete the statement.
20. Where P and Q are statements, the compound statement “P or Q” is known as a(n):
21. If two lines intersect, any two adjacent angles formed are:
22. If and are supplementary and Copyright Cengage Learning. Powered by Cognero.
, then must be a(n):
Page 4
Name: Class: Date: Practice Exam I
Subjective Short Answer
23. If m
24. and m
and 25. Let are complementary. Also, m
= 38.6° and .
and are vertical angles.Find m
and be a pair of adjacent angles for which m
and bisects , find m
.
26. Given that D-E-F on 27. , find m
and = 37° and m
= 49°. If , name the property that leads to the conclusion are supplementary. is acute. What type of angle is 28. When two parallel lines are cut by a transversal, and and , find x.
.
bisects .
?
are a pair of corresponding angles that are formed. If 29. Given line l, how many lines in space can be drawn parallel to l?
30. Using the symbols ∼ (for negation) and → (for implication), write the contrapositive of
the implication P → Q.
31. Write the first statement of the indirect proof for this statement:
“If coplanar lines l and m are not perpendicular to the same line t, then l and m are not parallel.”
32. In , m
= 37° and m
= 53°. What type of triangle is Copyright Cengage Learning. Powered by Cognero.
?
Page 5
Name: Class: Date: Practice Exam I
33. In , m
= 37° and m
= 116°. Find the measure of exterior angle RTV.
34. Find the sum of the interior angles for an octagon.
35. What two qualities are needed in order that a polygon be classified as a REGULAR polygon?
36. How many lines of symmetry does the square have?
Copyright Cengage Learning. Powered by Cognero.
Page 6
Name: Class: Date: Practice Exam I
Essay
37. Supply missing reasons for this proof.
Given: m || n
Prove: S1. m || n R1.
S2. S3. S4. R2.
R3.
R4.
Copyright Cengage Learning. Powered by Cognero.
Page 7
Name: Class: Date: Practice Exam I
38. Supply missing statements and missing reasons for the following proof.
Given: Prove: and transversal p; is a right angle
is a right angle
S1. and transversal p R1.
S2. R2.
S3. R3. Congruent measures have equal measures.
S4. R4.
S5. R5. Substitution Property of Equality
S6. R6. Definition of a right angle
39. Use an indirect proof to complete the following problem.
Given: Prove: (not shown)
and cannot both be right angles.
Copyright Cengage Learning. Powered by Cognero.
Page 8
Name: Class: Date: Practice Exam I
40. Use an indirect proof to complete the following problem.
Given: Prove: is not congruent to does not bisect 41. Supply missing statements and reasons for the foloowing proof.
Given: Prove: is supplementary to S1. R1.
S2. is supp. to R2. If the ext. sides of 2 adj. angles form a line, the angles are supp.
S3. R3. Angles supp. to the same angle are congruent.
S4. R4.
Copyright Cengage Learning. Powered by Cognero.
Page 9
Name: Class: Date: Practice Exam I
42. Supply missing statements and missing reasons for the following proof.
Given: also, Prove: so that bisects ;
S1. so that bisects R1.
S2. R2.
S3. R3. Given
S4. R4. If 2 angles of one triangle are congruent to
2 angles of a second triangle, then the third angles
of these triangles are also congruent.
43. Prove: Any two right angles are congruent.
Use the following drawing. Provide all statements and reasons.
Given: Right angles 1 and 2
Prove: Copyright Cengage Learning. Powered by Cognero.
Page 10
Name: Class: Date: Practice Exam I
44. Given: A-B-C-D as shown
Prove: Supply missing statements and missing reasons for this proof:
S1. R1.
S2. R2.
S3. R3. Segment-Addition Postulate
S4. R4. Substitution Property of Equality
45. Given: Prove: Provide the missing reasons for this proof:
S1. S2. S3. S4. S5. R1.
R2.
R3.
R4.
R5.
Copyright Cengage Learning. Powered by Cognero.
Page 11
Name: Class: Date: Practice Exam I
46. Given: In , is a right angle.
Prove: and are complementary.
;
Provide all statements and reasons for this proof.
47. Use an indirect proof to complete the following problem.
Given: Prove: and and are supplementary (no drawing)
are not both obtuse angles.
48. In the figure, x || y and transversal z. Explain why and must be supplementary.
49. Explain the following statement.
The measure of each interior angle of an equiangular triangle is 60.
Copyright Cengage Learning. Powered by Cognero.
Page 12
Name: Class: Date: Practice Exam I
50. Given: Prove: Supply all statements and reasons for the proof.
Copyright Cengage Learning. Powered by Cognero.
Page 13