The document contains examples of identifying the converse, inverse, and contrapositive of conditional statements. It also contains examples of identifying properties of equality like associative, commutative, distributive, substitution, and transitive properties. Additionally, it covers concepts like supplementary, complementary, and vertical angles and examples of finding supplements, complements, and using angle relationships to solve equations. The document concludes with examples of proofs involving solving equations for unknown variables.

1. What is the converse of the following statement:
If the sky is cloudy, then the sun is hidden.
a. If the sky is cloudy, then the sun is hidden.
b. If the sun is hidden, then the sky is cloudy.
c. If the sky is not cloudy, then the sun is not hidden.
d. If the sun is not hidden, then the sky is not cloudy.
What is the inverse of the following statement:
If you do your homework each night, then you will pass the test.
a. You do your homework each night.
b. You do not do your homework each night
c. You will pass the test.
d. You will not pass the test.
What is the contrapositive of the following statement:
If you do your homework each night, then you will pass the test.
a. You do your homework each night.
b. You do not do your homework each night
c. You will pass the test.
d. You will not pass the test.
What is the converse of the following statement:
If the Trojans score more points, then they win the game.
a. If the Trojans score more points, then they win the game.
b. If they win the game, then the Trojans score more points.
c. If the Trojans do not score more points, then they do not win the game.
d. If they do not win the game, then the Trojans do not score more points.
What is the inverse of the following statement:
If the Trojans score more points, then they win the game.
a. If the Trojans score more points, then they win the game.
b. If they win the game, then the Trojans score more points.
c. If the Trojans do not score more points, then they do not win the game.
d. If they do not win the game, then the Trojans do not score more points.
What is the contrapositive of the following statement:
If the Trojans score more points, then they win the game.
a. If the Trojans score more points, then they win the game.
b. If they win the game, then the Trojans score more points.
c. If the Trojans do not score more points, then they do not win the game.
d. If they do not win the game, then the Trojans do not score more points.

2. What is the converse of the following statement:
If the Americans have a good performance, then they will win a gold medal.
a. If the Americans have a good performance, then they will win a gold medal.
b. If they win a gold medal, then the Americans have a good performance.
c. If the Americans do not have a good performance, then they will not win a gold medal.
d. If they do not win a gold medal, then the Americans do not have a good performance.
What is the inverse of the following statement:
If the Americans have a good performance, then they will win a gold medal.
a. If the Americans have a good performance, then they will win a gold medal.
b. If they win a gold medal, then the Americans have a good performance.
c. If the Americans do not have a good performance, then they will not win a gold medal.
d. If they do not win a gold medal, then the Americans do not have a good performance.
What is the contrapositive of the following statement:
If the Americans have a good performance, then they will win a gold medal.
a. If the Americans have a good performance, then they will win a gold medal.
b. If they win a gold medal, then the Americans have a good performance.
c. If the Americans do not have a good performance, then they will not win a gold medal.
d. If they do not win a gold medal, then the Americans do not have a good performance.
Identify the following property of equality:
3x + 5y + 6 = 6 + 5y + 3x
a. Associative Property of Addition
b. Commutative Property of Addition
c. Transitive Property
d. Commutative Property of Multiplication
Identify the following property of equality:
5 + (a + 9) = (5 + a) + 9
a. Associative Property of Addition
b. Commutative Property of Addition
c. Transitive Property
d. Commutative Property of Multiplication
Identify the following property of equality:
If 3x = x + 9 and x + 9 = 4y, then 3x = 4y.
a. Associative Property of Addition
b. Commutative Property of Addition
c. Transitive Property
d. Commutative Property of Multiplication

3. Identify the following property of equality:
If a = b, then a + c = b + c
a. Substitution Property
b. Addition Property
c. Multiplication Property
d. Transitive Property
Identify the following property of equality:
If a = b, then a * c = b * c
a. Substitution Property
b. Addition Property
c. Multiplication Property
d. Transitive Property
Identify the following property of equality:
If x + 5 = 19 and x = 14, then 14 + 5 = 19.
a. Substitution Property
b. Addition Property
c. Multiplication Property
d. Transitive Property
Identify the following property of equality:
a ( b – c) = ab - ac
a. Distributive Property
b. Addition Property
c. Multiplication Property
d. Transitive Property
What is special about vertical angles?
a. They add up to 180°
b. They add up to 90°
c. They are supplementary
d. They are the same

4. What is special about supplementary angles?
a. They add up to 180°
b. They add up to 90°
c. They are across from each other
d. They are the same
What is special about complementary angles?
a. They add up to 180°
b. They add up to 90°
c. They are across from each other
d. They are the same
What is the supplement of an angle that is 81°?
a. 9°
b. 180°
c. 99°
d. 81°
What is the supplement of an angle that is (x + 9)°?
a. (189 – x)°
b. (189 + x)°
c. (171 – x)°
d. (171 + x)°
What is the complement of an angle that is 13°?
a. 167°
b. 67°
c. 90°
d. 180°

5. What is the complement of an angle that is (2x - 10)°?
a. (100 + 2x)°
b. (100 – 2x)°
c. (80 + 2x)°
d. (80 – 2x)°
The measure of an angle is 12 more than the measure of its complement. Find x.
a. 36°
b. 37°
c. 38°
d. 39°
The measure of an angle is three times more than the measure of its supplement. Find x.
a. 45°
b. 50°
c. 40°
d. 135°
The measure of an angle is 10 less than the measure of its supplement. Find x.
a. 100°
b. 95°
c. 85°
d. 135°
If m<1 and m<2 are vertical and m<1 = 6x + 10 and m<2 = 12x – 2, find m<1.
a. 16°
b. 22°
c. 30°
d. 28°
Complete the following proofs on the lined portion of your scantron.
34. Given: 3x + 19 = 9x – 11. Prove x = 5. 35. Given -5x + 10 = 7x – 2. Prove x = 1.

6. 36. Given: 2( m – 6) = 20. Prove m = 16. 37. Given 4x + 12 = y - 2. Given x = -2.
Prove y = 6.