Download Geometry Ch 2 Review 1. Points D, G, and F are collinear. ABH ∠ is

Geometry Ch 2 Review
Use the diagram to determine whether the statement is true or false.
1. Points D, G, and F are collinear.
2. ABH is a right angle.
3. ABH and CBH are complementary.
4. IH is perpendicular to line m.
5. DEH and FEH are supplementary.
6. CB is perpendicular to line ℓ.
Determine whether the conditional statement is true. If false, give a counterexample.
7. If two planes intersect, then they intersect in exactly one point.
8. If two lines intersect, then they form four angles.
Write the converse and inverse of the statement.
9. If it is Sunday, then it is the weekend.
10. If m A  95, then  A is obtuse.
11. If an animal is a bird, then it has two eyes.
Decide whether inductive reasoning or deductive reasoning is used to
reach the conclusion.
12. Gas prices have gone up every day this week. The price of gas will go
up tomorrow.
13. What goes up must come down. The ball went up. It will come down.
Use the Law of Detachment to determine what you can conclude from
the given information, if possible.
14. If three points lie on the same line, they are collinear. Points A, B, and C
lie on line .
15. If it is hailing, then you are not going outdoors. It is hailing.
Use the Law of Syllogism to draw a conclusion to write a new conditional statement that follows from the
pair of true statements, if possible.
16. If a quadrilateral is a square, then it has four right angles. If a quadrilateral has four right angles, then it is a
rectangle.
17. If a number ends in 0, then it is divisible by 10. If a number is divisible
by 10, then it is divisible by 5.
Solve the equation. Justify each step.
18.
x3
 8
2
19. 5x  3  4 x  2
20.You and your brother borrowed money to buy a car from a local bank at an annual simple interest rate of 5%.
The amount of interest I is represented by the equation I  Prt where P is the principal amount, r is the rate
(in decimal form), and t is the time (in years). Solve the formula for P, then find the principal amount when the
interest is $7500 and the time is 6 years. Be sure to justify each step.
Identify the property that justifies the statement.
22. 614  614
21. KL  PR, so PR  KL
23. If a  b and b  c, then a  c.
24. Let p be “an animal is a puppy” and let q be “it is a dog.” Write each statement
in words. Then decide whether it is true or false.
a. the conditional statement p  q
b. the converse q  p
c. the inverse ~ 𝑝 → ~ 𝑞
d. the contrapositive
~𝑞 → ~𝑝
Write a proof using any format.
25. Given 1 and 2 are supplementary, m1  135
Prove m2  45
Write a 2-column proof.
26. Given m1  m2  90,
m3  m4  90
Prove m1  m4
Geometry Ch 2 Review Answers
1. false
2. true
3. False
4.
true
5.
true
6.
true
7. false; If two planes intersect, then their intersection is a line. Plane Intersection Postulate (Post. 2.7).
8. true
9. converse: If it is the weekend, then it is Sunday; inverse: If it is not Sunday, then it is not the weekend.
10. converse: If A is obtuse, then mA  95; inverse: If mA  95 , then A is not obtuse.
11. converse: If an animal has two eyes, then it is a bird; inverse: If an animal is not a bird, then it does not have two eyes.
12. inductive reasoning
13.
deductive reasoning
14.
Points A, B, and C are collinear.
15. You are not going outdoors.
16.
If a quadrilateral is a square, then it is a rectangle.
17. If a number ends in 0, then it is divisible by 5.
18. x  19;
19. x   5;
x 3
 8
2
Given
x  3  16
Multiplication Property
of Equality
x  19
20. P 
Subraction Property
of Equality
I
; $25000;
rt
I  Prt
Given
5x  3  4 x  8
Distributive Property
x  3  8
x  5
Subraction Property
of Equality
Addition Property
of Equality
21. Symmetric Property of Segment
Given
7500  P0.056
Substitution Property
of Equality
7500  0.3P
Simplify.
25,000  P
5 x  3  4 x  2
Congruence
(Thm. 2.1)
22. Reflexive Properties of Equality
23. Transitive Properties of Equality
Division Property
of Equality
24. a. conditional: If an animal is a puppy, then it is a dog; true
b. If an animal is a dog, then it is a puppy; false
25.
26.
c. If an animal is not a puppy, then it is not a dog; false
STATEMENTS
REASONS
d. If an animal is not a dog, then it is not a puppy; true
1. m1  m2  90
1. Given
2. m3  m4  90
2. Given
STATEMENTS
REASONS
1. 1 and 2 are
supplementary.
1. Given
3. m1  m2 
m3  m4
3. Transitive
Property of
Equality
2. m1  135
2. Given
4. m2  m3
4. Vertical Angles
3. m1  m2  180
3. Definition of
supplementary
angles
5. m1  m2 
m2  m4
5. Substitution
Property of
Equality
4. 135  m2  180
4. Substitution
Property of
Equality
6. m1  m4
6. Subtraction
Property of
Equality
5. m2  45
5. Subtraction
Property of
Equality