Download Name_________________ Date___________ Geometry Chapter 2

Name_________________
Date___________
Geometry
Chapter 2 Review
1.) Given the statement: If a figure is a kite, then it is a rhombus.
Write the following:
A.) contrapositive
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B.) inverse
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C.) converse
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2.) A.) Find the next item in the pattern. 1, 2, 3, 5, 8, 13, . . .
B.) Describe the pattern in words.
3.) Is the statement below true or false? If it is false give a counterexample to justify the conclusion.
The difference of two odd numbers is a prime number.
4.) Identify the hypothesis and conclusion of the statement
“If an angle has a measure less than 90, then the angle is acute.”
A.) Hypothesis
B.) Conclusion
For numbers 5-7 state whether the conjecture is valid or invalid with the given information. If it is valid
state whether it is by the Law of Detachment or the Law of Syllogism .
5.) Given: If a ray bisects an angle, two congruent angles are formed.

YW bisects XYZ.
Conjecture: XYW  WYZ
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6.) Given: If a number is a prime number, then it is an odd number. If a number is not divisible
by 2, then it is an odd number. Conjecture: If a number is not divisible by 2, then it is a
prime number.
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7.) Given: If a whole number ends in 0, then it is divisible by 2. If a whole number is divisible by 2, then it is
even. Conjecture: If a whole number ends in 0, then it is an even number.
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8. Write the definition as a biconditional.
A square is a rectangle with four congruent sides.
9.) Give the condition statement, If is a dog then is a four legged animal.
A.) Is the condition true or false.
B.) Write the converse.
C.) Is the converse true or false.
D.) Write a biconditional statement from the condition and the converse.
E.) Is the statement in part D true or false.Why?
10.) Solve the equation. Write a justification for each step.
5m  4  3(x -8)
11.)Use the Symmetric Property of Congruence to complete the statement
“If ABC  XYZ, then XYZ  _________.”
12.Draw a picture and fill in the blanks for the 2 column proof below.
Given: ABC is a right angle, X is in the interior of ABC, and mXBC  45.
Prove: BX bisects ABC.
Picture
Proof:
Statements
Justification
1. ABC is a right angle.
1. _____________
2.
2. Def. of rt. 
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3. X is in the interior of ABC.
3. _____________
4. mABX  mXBC  mABC
4.  Add. Post., Steps 1, 3
5. mXBC  45
5. Given
6. mABX  45  90
6.
7. mABX  45
7. Subtr. Prop. of 
8. ABX  XBC
8. Def. of  ?
9. BX bisects ABC.
9. _______________
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13.) Fill in the blanks for the 2 column proof below.
Given: O is the midpoint of MP
P is the midpoint of
Prove:
OE
MO  PE
Statement
1. O is the midpoint of MP
2. MO = OP
3. P is the midpoint of
OE
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5. MO = PE
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Justification
1._________________________________
2.__________________________________
3._________________________________
4.Definition of a Midpoint.
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6. Definition of Congruence
14.) Draw out a flow chart proof for the proof in question 13.
15.)Given: B and C on circle Q,
C is the midpoint of QE
Prove: BQ = EC