Download Name: Geometry, ______ Geometry Ch. 1 Review 1. Draw 3 points

Name:________________________________
Geometry, ___________
Geometry
Ch. 1 Review
1. Draw 3 points A, B, and C so that they are not collinear. Using these points, draw
AB ,
BC , and AC .
2.
a) True or False: Points F,A, and B are coplanar?
b) True or False: Points G, E, O, and B are
coplanar?
c) True or False: Points F, A, L, and O are
coplanar?
d) True or False: Points G, E, and O are collinear?
e) True or False: Points G, and A are collinear?
3. Fill in the blank with always, sometimes, or never.
a) Two points are _____________________ collinear.
b) Three points are _____________________ collinear.
c) Three points are ____________________ coplanar.
d) Four points are _____________________ coplanar.
e) If two distinct lines intersect, then they _______________ intersect in exactly one point.
f) If two distinct planes intersect, then they ________________ intersect in exactly one line.
g) Adjacent angles are ________________ complementary.
h) Vertical angles are _______________________ congruent.
i) The sum of a linear pair is __________________ 90 degrees.
j) Complementary angles _________________ add up to 180 degrees.
4. Use the figure to answer these questions.
a. Name a point that is coplanar with points U, X, and W.
b) Name a point that is coplanar with points U, V, and S.
c) Name the intersection of the planes XUV and UQT.
5. Use the number line below to answer these questions.
a) What is the coordinate for P?
b) Find PQ.
c) Is LM  NP ? Justify your answer.
6. Using the diagram below, if RS  4 x  10 , ST  x , and RT  30  x , then what is RT?
7. A is the midpoint of BN . If AB  6 , then what is AN and BN?
8. Draw an obtuse angle ABC . Be sure to properly name the angle.
9. Use your protractor to measure LGA .
A
G
L
10. On the diagram below, if mABC  (5x) , mCBZ  40 , and mABZ  (2 x  20) .
Find x and the measures of angles ABZ and CBZ.
11. If mC  40 , then what is the supplement of angle C?
12. Find the missing measures of the angles in the diagram below.
1
30 95
2
3
13. ABC and TBC are a linear pair. If mABC  58 , then what are the measures of
TBC and ABT .
14. JK is the angle bisector for AJP . If mAJK  x , mAJP  (3x  40) ,
mPJK  40 then find mAJK and mAJP .
15. Using the figure below, if mAOB  (40  x) , mBOC  35 , and mCOD  (60  x) ,
then find the measures of COD and AOD .
16. For AB , A has a coordinate of 4 and B has a coordinate of -8 on the x-axis. Find the
coordinate for the midpoint of AB .
17. A has coordinates of (1 , 4) and B has coordinates of (-5 , 2). Find the coordinates for the
midpoint of AB .
18. The midpoint of PR is at (4 , 7). If P has coordinates of (6 , 10), what are the coordinates of
R?
19. For AB , A has coordinates of (1 , 3) and B has coordinates of ( -4 , 1). What is AB?
Name:_______________________________________
Mr. Cereghino
Geometry, ____________
Geometry
Ch. 2.1-2.3 Review
1. Rewrite the statement in if-then form.
A queen bumble bee lives for one year.
2. Decide whether the statement is true or false. If false, provide a counterexample.
a) If 3 points are coplanar, then they are collinear.
b) If I live in Texas, then I live in Dallas.
c) If m1  32 , then 1 is acute.
3. What is the minimum number of points needed to create a distinct line?
4. What is the minimum number of points needed to create a distinct plane?
5. Write the converse, inverse, and contrapositive of the statement below. Then indicate which
statements are true and false.
If it is Saturday, then I will not have school.
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
6. Determine whether the biconditional statement is true or false. If false, provide a
counterexample.
a) 3 points are collinear if and only if they are coplanar.
b) 2 angles are a linear pair if and only if they are supplementary.
c) An angle is right if and only if its measure is 90 degrees.
7. Can the following statement be written as a true biconditional statement? If so, write the
statement as a true biconditional statement. If not, give a counterexample.
a) Owls live in trees.
b) Supplementary angles are 2 angles which add up to 180 degrees.
c) Vertical angles are congruent.
8. Using p and q below, write the symbolic statement in words.
p = we win our game
q = we will not have practice tomorrow
a) ~p
b) ~q
c) p  q
d) ~ p  ~ q
9. Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain
your answer.
a) Johnny goes to a zoo and sees that all the swans are white. Johnny concludes that all swans
are white.
b) Johnny is told he has a right angle. Johnny concludes that the angle must then be 90 degrees.
10. State whether the argument is valid. Explain your reasoning.
a) Susan knows that all sophomores must take driver’s education. Tommy takes driver’s
education so Susan concludes that Tommy must be a sophomore.
b) Joe knows that shapes with 4 sides are called quadrilaterals. Joe knows that a square has 4
sides so he concludes that it must be a quadrilateral.
11. The bulleted if-then statements are true. Use the Law of Syllogism to fill in the blank below.




If we go to the park, then we will play baseball.
If I do my chores, then I will go to my friend’s house.
If we play baseball, then I will hit a homerun.
If I go to my friend’s house, then we will go to the park.
If I do my chores, then ____________________________________________________
12. Assume the following statements are true.




If Susan screams, then the dog will run away.
If the dog licks Susan, then Susan will scream.
If Carl tells the dog to “kiss,” then the dog will lick Susan.
Carl tells the dog to “kiss.”
a) Write the premises in an order which makes a valid argument.
b) Did the dog lick Susan? Explain.
c) Did the dog run away? Explain.
13. Assume the following statements are true.




If I call the superintendent, then I must pay rent.
If the apartment ceiling is not leaking, then it is not raining.
I will call the superintendent if the apartment ceiling leaks.
If it is not raining, then it is not Tuesday.
a) Write the statements in order which makes a valid argument.
b) It is Tuesday, can you conclude that you must pay rent? Explain.
c) It is not Tuesday, can you conclude you did not pay rent? Explain.