Name
CP Geometry
1.)
Date
Chapter 2 Review
PD
̅̅̅̅̅, 𝑴𝑵
̅̅̅̅̅, 𝐚𝐧𝐝 𝐋𝐍
̅̅̅̅.
Suppose M is between L and N. Solve for y. Then find the lengths of 𝑳𝑴
1
LM = 3 𝑦 + 4
2
MN = 2𝑦 + 3
8
LN = 3 𝑦 + 1
2.)
Use the diagram at the right to find the missing angles.
𝑚∠𝐺𝑋𝐴 =
54º
𝑚∠𝐸𝑋𝐺 =
38º
𝑚∠𝑁𝑋𝐴 =
3.)
Make sure you can define the following vocabulary words.





Point
Line
Plane
Segment
Endpoint




Ray
Opposite rays
Initial point
Bisect


Congruent
angles
Congruent
segments
Using the Laws of Detachment and Syllogism, write the conclusion of each logical argument.
4.)
If an angle measures more than 90°,
then it is not acute.
𝑚∠𝐴𝐵𝐶 is 115°.
5.)
If you order dessert, then you will have a
slice of apple pie.
If you have a slice of apple pie, then you
will drink a glass of milk.
____________________________________
_________________________________
1-Write each type of statement in symbolic notation AND in if-then form. 2-Indicate whether it is true or false. 3-Provide a
counterexample or write NONE where applicable.
Statement: 𝒙𝟒 = 𝟏𝟔, 𝒊𝒇 𝒙 = 𝟐
#
6.
Type of
statement
Conditional
7.
Inverse
8.
Converse
9.
Contrapositive
10.
Biconditional
Symbolic
Notation
Example in if-then form
True/ Counterexample
False
Statement: A linear pair is supplementary.
#
Type of
statement
11.
Conditional
12.
Inverse
13.
Converse
14.
Contrapositive
15.
Biconditional
Symbolic
Notation
Example in if-then form
True/ Counterexample
False
Each statement below is an example of one of the properties you learned in Chapter 2. State the property
represented. (For the conditional statements, state the property you would use to go from the hypothesis to
the conclusion.)
16. ̅̅̅̅
𝑋𝑌 ≅ ̅̅̅̅
𝑋𝑌
17. If mB  45  , then 40   mB  85  .
18. If x = 15, then 15 = x.
19. If RS = TU and TU = VW, then RS = VW.
20. If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.
21. If mM  70  , then 2(mM )  140  .
22. ∠𝐴𝐵𝐶 ≅ ∠𝐴𝐵𝐶
23. If GH + IJ = KL + IJ, then GH = KL.
24. If x = 5 and y = 18 – x , then y = 13.
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅, then 𝐶𝐷
̅̅̅̅ ≅ 𝐴𝐵
̅̅̅̅
25. If 𝐴𝐵
Use the diagram to give an example of each postulate.
26. If two lines intersect, then their intersection
is a point.
27. Through any two points there is exactly one
line.
28. If two points lie in a plane, then the line
containing them lies in the same plane.
29. If two planes intersect, then their
intersection is a line.
30. A plane contains at least 3 noncollinear
points.
Solve for x and give a reason for each step. Don’t forget your reason for your first step.
31.)
32.)
(9 x  14) 
(4 x  11) 
(6 x  10) 
(5x  54) 
Statements
Reasons
Statements
Reasons
Fill in the missing statements and reasons of the proof.
33.)
GIVEN: 3 and 4 are complement ary.
1  3, 2  4
4
1
2
3
PROVE: 1 and 2 are complement ary.
STATEMENTS
REASONS
1.
1. Given
2.
2. Definition of Complementary Angles
3. 1  3, 2  4
3.
4. m1  m3, m 2  m4
4.
5. m1  m4  90 
5. Substitution Property of Equality
6. m1  m2  90 
6.
7.
7.