Download 2.1-2.4 Review Packet Solutions

Geometry
2.1-2.4 Review WS
Name________________________________
Date_____________________Period______
ANSWER KEY
#1-2: Show the conjecture is false by finding a counterexample.
1. If the product of two numbers is positive, then the two numbers must be positive.
(answers will vary)
(-4) x (-3) = 12
2. The sum of any two prime numbers is always even.
1+2=3
#3: For the given statement, write the if-then form, the converse, the inverse, and the contrapositive.
3. The measure of a straight angle is 180°
If-Then: If an angle is straight, it measures 180°.
Converse: If an angle measures 180°, then it is straight.
Inverse: If an angle is not straight, then it does not measure 180°.
Contrapositive: If an angle does not measure 180°, then it is not straight.
4. Sketch the fourth figure in the pattern below.
5. Write the next three numbers in the pattern: 2, 4, 8, 16, …
32, 64, 128 (multiply by 2 each time)
#6-8: Find a counterexample to disprove the conjecture.
6. All intersecting lines form right angles.
7. All quadrilaterals are equilateral.
8. All triangles are regular.
#9-12: Use the true statements below to determine whether you know the conclusion is true or false.
Explain your reasoning.
If Dan goes shopping, then he will buy a pretzel.
If the mall is open, then Jodi and Dan will go shopping.
If Jodi goes shopping, then she will buy a pizza.
The mall is open.
9. Dan bought a pizza.
10. Jodi and Dan went shopping
FALSE
11. Jodi bought a pizza.
TRUE
12. Jodi had some of Dan’s pretzel.
TRUE
FALSE
#13-16: Label the following planes and points appropriately.
A
13. Label the vertical plane as A and the horizontal plane as B.
14. Draw two points 𝑋 and 𝑌 on the diagram so they lie in plane 𝐴, but not
in plane 𝐵.
15. Draw point 𝑍 on the diagram so it lies in both plane 𝐴 and plane 𝐵.
⃡ is the intersection of
16. Plot points 𝑄 and 𝑅 on the diagram so that 𝑄𝑅
plane 𝐴 and plane 𝐵.
R
Y
Z
B
Q
X
17. If point 𝐵 is the midpoint of ̅̅̅̅
𝐴𝐶 , then point 𝐵 bisects ̅̅̅̅
𝐴𝐶 . If point 𝐵 bisects ̅̅̅̅
𝐴𝐶 , then ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 . Using the
Law of Syllogism, what conclusion can be drawn?
̅̅̅̅ , then 𝐴𝐵
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
a. If point 𝐵 if the midpoint of 𝐴𝐶
̅̅̅̅
̅̅̅̅
̅̅̅̅
b. If 𝐴𝐵 ≅ 𝐵𝐶 , then point 𝐵 bisects 𝐴𝐶 .
c. If ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 , the point 𝐵 is the midpoint of ̅̅̅̅
𝐴𝐶 .
A
C
B
d. Points 𝐴, 𝐵, and 𝐶 are collinear.
18. Which statement is not a point, line, or plane postulate?
a. A plane contains at least 3 noncollinear points.
b. If 2 lines intersect, then their intersection is exactly 1 point.
c. A line contains at least 2 points.
d. Coplanar points are points that lie on the same plane.
#19-22: Determine if statement (3) follows from statements (1) and (2) by either the Law of Detachment of
the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.
19. (1) If an angle measures more than 90°, then it is not acute.
(2) 𝑚∠𝐴𝐵𝐶 = 120°
(3) ∠𝐴𝐵𝐶 is not acute.
20. (1) All 45° angles are congruent.
(2) ∠𝐴 ≅ ∠𝐵
(3) ∠𝐴 and ∠𝐵 are 45° angles.
YES, DETACHMENT
NO, INVALID
21. (1) If you order the apple pie, then it will be served with ice cream.
(2) Matthew ordered the apple pie.
(3) Matthew was served ice cream.
22. (1) If you wear the school colors, then you have school spirit.
(2) If you have school spirit, then the team feels great.
(3) If you wear the school colors, then the team will feel great.
YES, DETACHMENT
YES, SYLLOGISM