Download ch 2 test review

Chapter 2 Geo Test REVIEW (Not Worth pts)
Name ______________________
1. Make a conjecture about the next object in this sequence.
2. Identify the conclusion of the statement If an animal is a bird, then the animal has wings.
______ 3. Which best describes the statement If two lines intersect, then their intersection is a point?
a) always true
b) sometimes true
c) never true
d) cannot tell
______ 4. Which best describes the statement A plane contains three points?
a) always true
b) sometimes true
c) never true
d) cannot tell
Name the property that justifies each statement.
5. If 3(x + 2) = 15, then 3x + 6 = 15.
7. x = x
6. If A  B and B  C, then A  C
8. If XY  TZ then TZ  XY
9. If x = 3 and xy = 12, then 3y = 12.
10. If ABD  FGH and mABD = 137,
find mJGH.
11. If mABC = 48 and mABC  mDBE,
find mDBC.
12. Find mFAD if mBAC = 62.
13. If m2= 2x + 21 and mBAC = 6x, find x.
State the definition, property, postulate, or theorem that justifies each statement.
14. If two angles form a linear pair, then they are supplementary angles. _________________________________
15. If mC = mD, then C  D. ________________________________
16. If X is the midpoint of YZ , then YX  ZX . _________________________________________
17. If M is between D and P, then DM + MP = DP. _________________________________________
18. Complete the proof by supplying the missing information. If
Statements
1.
x2

5


3 , then x = –17.
Reasons
1. Given
3
x  2 
2. 5

 5 
x2

5
 35
2. ____________________

3. Substitution
3. x + 2 = –15
4. _________________
4. x + 2 – 2 = –15 – 2
5. x = –17
19. Given: 5x + 3(8 – 2x) = 6 + 8x
5. Substitution
Prove: x = 2
Statements
1. 5x + 3(8 – 2x) = 6 + 8x
Reasons
1. Given
2. 5x + 24 – 6x = 6 + 8x
2. _____________________
3. 24 – 1x = 6 + 8x
3. Substitution (Addition of like terms)
4. 24 = 6 + 9x
4. ______________________
5. 9x = 18
5. ______________________
6. x = 2
6. ______________________
20. Given: 1  2
Prove: 3  4
Statements
1. 1  2
Reasons
1. ______________________
2. m1 + m3 + m5 = 180
2. _______ ___________ Postulate
3. m1 + m3 + 90 = 180
3. Substitution
4. m1 + m3 = 90
4. ______________________
5. m4 + m2 = m5
5. ___________ _______ Thm
6. m4 + m2 = 90
6. Substitution
7. m4 + m1 = 90.
7. Substitution
8.
3  4
8. ______________________
21. Write the statement in if-then form: The intersection of two planes is a line.
22. Write the converse of the conditional statement. Then determine whether the converse is true or
false. If it is false, find a counterexample: If an animal is a Dalmatian, then it is spotted.
23. Write the contrapositive of the conditional statement: If two angles are vertical, then they are congruent.
24. Write the inverse of the conditional statement: All whole numbers are integers.
Make a conjecture about the next item in the sequence.
25. 15, 30, 45, 60, Next term: _______ Rule in words: ___________________________________
26. 80, –40, 20, –10, Next term: ________
Rule in words: ____________________________________
27. If m3 = 7x + 10 and m4 = 5x + 24, find m4.
Work:
x = _____ and m4 = __________
Use the figure at the right. State the postulate that can be used to show each statement is true.
28. Points R, O , and T are in plane RNP.
29. Line SO is contained in plane UNP.
30. If m4 = 42, then find the m1. Explain how you know this is true.
31. Given the information below, EXPLAIN what theorem(s) you would use to find the measure of 13.
Then show your work and find m13.
m13 = x + 2 and m14 = 5x + 10
Work:
Explanation with theorem(s):
m13 = _________
32. If A, B, and C are collinear and AB = 3, BC = 9, and AC = 6, EXPLAIN how you can determine which point is
between the other two?
Point ____ is between ___ and ___ because _______________________________________________
Answers: 1.
6. Transitive
2. The animal has wings
7. Reflexive
8. Symmetric
13. 8x + 21 = 90, x = 8.62514. supp thm
17. Segment add post
3. A
9. Substitution
4. B
5. Distributive
10. 43
15. Def of congruent angles
18. Multiplication, subtraction
11. 84
12. 28
16. Midpt thm
19. Distributive, addition, subtraction, division
20. given, angle addition post, subtraction, vertical angle them, congruent complements thm
21. If 2 planes intersect, then their intersection is a line
22. If an animal is spotted, then it is a Dalmatian. False, leopard, cow, etc
23. If 2 angles are not congruent, then they are not vertical angles
24. If a number is not a whole number, then it is not an integer
25. 75, add 15 to the previous term
27. 7x + 10 = 5x + 24, x = 7, 59
26. 5, Divide previous term by -2
28. Through 3 noncollinear points there is exactly 1 plane
29. If 2 points lie in a plane, then the entire line containing the points lies in the plane
30. 42 by the vertical angle thm
31. Comp thm, 6x + 12 = 90, x = 13, 15
32. A is between B and C. The biggest distance is between the 2 endpoints.