1. Chapter 2 Quiz Review

2. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: Two angles are supplementary.
Conjecture: They are a linear pair.

3. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: 58=2 𝑥 2 +8
Conjecture: 𝑥=5

4. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: ∠𝐴 and ∠𝐵 are vertical angles
Conjecture:∠𝐴≅ ∠𝐵

5. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: 𝑋𝑌 = 𝑌𝑍
Conjecture: 𝑌 is the midpoint of 𝑋𝑍

6. Make a conjecture about the next item in the following sequences.
-5, 15, -45, 135
1, 8, 27, 64, 125
22, 16, 10, 4, -2

7. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
𝐴𝑇 and 𝑀𝑁 intersect at plane L

8. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
Non-collinear points A, B, and C form a plane

9. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
Points S, T, and U determine three lines

10. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
If points A, B, and C lie in plane M, then they are collinear.

11. Write the statement in if-then form
Write the statement in if-then form. Then write the converse, inverse, and contrapositive.
An angle bisector forms two congruent angles.

12. Write the statement in if-then form
Write the statement in if-then form. Then write the converse, inverse, and contrapositive.
Adjacent angles have a common side.

13. Write a two column proof.
Given: − 1 2 𝑚−3=6 Prove: 𝑚=−18

14. Write a two column proof.
Given: 𝟑𝒙+𝟓 𝟐 =𝟕 Prove: 𝒙=𝟑

15. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: Two angles are supplementary.
Conjecture: They are a linear pair.
False. They could be two separate non-adjacent angles, with one measuring 40 degrees and the other measuring 140 degrees.

16. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: 58=2 𝑥 2 +8
Conjecture: 𝑥=5
False. x can also be equal to -5.

17. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: ∠𝐴 and ∠𝐵 are vertical angles
Conjecture:∠𝐴≅ ∠𝐵
True!

18. Determine if the following conjecture is true or false
Determine if the following conjecture is true or false. Give a counterexample if false.
Given: 𝑋𝑌 = 𝑌𝑍
Conjecture: 𝑌 is the midpoint of 𝑋𝑍
False. The points do not have to be collinear. Z Y X

19. Make a conjecture about the next item in the following sequences.
-5, 15, -45, 135, -405
1, 8, 27, 64, 125, 216 (𝟔 𝟑 )
22, 16, 10, 4, -2, -8

20. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
𝐴𝑇 and 𝑀𝑁 intersect at plane L
Never. If two lines intersect, their intersection is a point.

21. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
Non-collinear points A, B, and C form a plane
Always. Through any three non-collinear points, there is exactly one plane.

22. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
Points S, T, and U determine three lines
Sometimes. A line has at least two points so they all could be collinear, but through any two points there is exactly one line so you could get lines ST, TU, and SU.

23. Determine whether each statement is always, sometimes, or never true
Determine whether each statement is always, sometimes, or never true. EXPLAIN.
If points A, B, and C lie in plane M, then they are collinear.
Sometimes. Through any three non-collinear points, there is exactly one plane, but there could be other points and these could be collinear and on plane M.

24. Write the statement in if-then form
Write the statement in if-then form. Then write the converse, inverse, and contrapositive.
An angle bisector forms two congruent angles.
If-Then: If a line is an angle bisector, then it forms two congruent angles. (TRUE)
Converse: If a line forms two congruent angles, then it is an angle bisector. (TRUE)
Inverse: If a line is not an angle bisector, then it does not form two congruent angles. (TRUE)
Contrapositive: If a line does not form two congruent angles, then it is not an angle bisector. (TRUE)

25. Write the statement in if-then form
Write the statement in if-then form. Then write the converse, inverse, and contrapositive.
Adjacent angles have a common side.
If-Then: If the angles are adjacent, then they have a common side. (TRUE)
Converse: If they have a common side, then the angles are adjacent. (FALSE; overlapping angles)
Inverse: If the angles are not adjacent, then they do not have a common side. (FALSE; overlapping angles)
Contrapositive: If they do not have a common side, then the angles are not adjacent. (TRUE)

26. Write a two column proof.
Given: − 1 2 𝑚−3=6 Prove: 𝑚=−18
Statements
Reasons
1. − 1 2 𝑚−3=6
1. Given
2. − 1 2 𝑚=9
2. Addition Property of Equality
3. −𝑚=18
3. Multiplication Property of Equality
4. 𝑚=−18
4. Division Property of Equality

27. Write a two column proof.
Given: 𝟑𝒙+𝟓 𝟐 =𝟕 Prove: 𝒙=𝟑
Statements
Reasons
1. 𝟑𝒙+𝟓 𝟐 =𝟕
1. Given
2. 3𝑥+5=14
2. Multiplication Property of Equality
3. 3𝑥=9
3. Subtraction Property of Equality
4. 𝑥=3
4. Division Property of Equality