Download Geometry A Name Unit 2 Review Geoff is really excited to learn

Geometry A
Unit 2 Review
Name
1. Geoff is really excited to learn about triangles next week. Over the weekend, he is
exploring different triangles and their angle measures. After exploring many triangles, he
notices a pattern. All of the measures of the angles inside the triangle seem to sum to
180 degrees. Using
reasoning, he makes a
that the angles in a triangle always sum to 180 degrees.
Using
reasoning and Mrs. Gerrish’s help, he proves the
conjecture to be true.
2. Write the converse, inverse, and contrapositive of the following conditional. Then,
determine their truth value.
“If we have a snow day, then school is closed.”
T/F:
Hypothesis:
Conclusion:
Converse:
T/F:
Inverse:
T/F:
Contrapositive:
T/F:
3. Determine if each statement is true or false. If the statement is false, give a
counterexample.
a. If the month is February, then there are 28 days in the month.
b. If x  6 , then x 2  36 .
c. If x 2  36 , then x  6 .
d. If 2+2=5, then it rains cats and dogs.
e. If it is a flower, then it is a daisy.
f. If Zach wins the lottery, then he will give everyone in Geometry class $1000.
(he didn’t)
4. Write the definition as a biconditional.
“An idiot is an utterly foolish or senseless person.”
(dictionary.reference.com)
T
5. Determine if the biconditional statement is true or false. If it is true, explain why. If it is
not, explain why not.
“Angles are congruent if and only if they are vertical angles. “
6. Determine if the conclusion is valid using the Law of Detachment.
If you mow the neighbor’s yard, then you will earn $20.
Jared has $20.
Conclusion: Jared mowed the neighbor’s yard.
Given:
Valid
Invalid
7. Complete the conclusion based on the Law of Syllogism.
If you mow the neighbor’s yard, then you earn $20.
If you earn $20, then you will go to the movies.
Conclusion: If you mow the neighbor’s yard, then
Given:
8. Write the algebra proof.
Given:
2( x  4)  4 x  5 x  10
Prove:
x  6
Statement
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reason
.
9. Complete the proof.
Given:
SR bisects QST
mQSR   3 x  5  , mRST   2 x  9 
Prove:
mQST  74
Statement
Reason
1. SR bisects QST
2. mQSR   3 x  5  , mRST   2x  9 
3. QSR  RST
4. mQSR  mRST
5. 3x  5  2x  9
6. 3 x  2x  5  2x  2x  9
7. x  5  9
8. x  5 5  9 5
9. x  14
10. mQSR   3  14  5  , mRST   2  14  9 
11. mQSR  37 , mRST  37
12. mQSR  mRST  mQST
13. 37  37  mQST
14. 74  mQST
15. mQST  74
10. Write the proof of the Right Angle Congruence Theorem.
Given:
Prove:
Statement
1.
2.
3.
4.
Reason
11. Write the proof of the Linear Pair Theorem.
Given:
Prove:
Statement
Reason
1.
2.
3.
4.
5.
6.
7.
8.
9.
12. Complete the proof of the Congruent Complements Theorem.
Given:
1 and 2 are complementary
2 and 3 are complementary
Prove:
1  3
Statement
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reason
Given
Definition of complementary angles
Given
Transitive Property of Equality
m2  m2
m1  m2  m2  m2  m2  m3
Simplify
13. Given the diagram below, find all the pairs of…
a. corresponding angles
b. vertical angles
c. linear pairs
d. alternate interior angles
e. alternate exterior angles
f. same-side interior angles
14. Use the parallel line theorems to find the missing angle. Be sure to state which
theorem/postulate you used.
a. Find mKLM .
b. Find mDEF
c. Find mQRS .
d. Find the value of x that would make m n .
(6x + 5)º
m
(5x - 12)º
n
15. Determine if the following relationships prove that the lines are parallel. If so, you should
have a theorem/postulate that supports it. If not, determine if there is “not enough info” or
“not parallel”.
1. m3  150 , m6  30
2. m4  90 , m5  90
3. 4  8
4. 1  3
5. m4  50 , m6  50
6. m2  80 , m8  80
7. m6  40 , m3  120
8. m5  115 , m6  65
9. 4  7