Download Key Geometry with Measurement Name:_____ Date:______ Period

Geometry with Measurement
Chapter 2 Review
Key
Name:___________________ Date:______ Period:___
Use inductive reasoning to describe each pattern and find the next two terms of each
sequence.
1. 1, 8, 27, 64, 125…
pattern:
# cubed
next two: 216, 343
2. 0, 1, 1, 2, 3, 5, 8, 13…
pattern: add new # to previous next two: 21, 34
Write the converse, inverse, and contrapositive for each statement. Determine the truth
value for each (either true or false). Give counter example for any FALSE statements.
3. If two angles are a vertical pair then the two angles are congruent.
converse If two angles are congruent then the angles are a vertical pair.
truth value false
counter example __40
40 angles equal but don’t form an X.
inverse If two angles are not a vertical pair then the angles are not congruent.
truth value false
counter example see above example
contrapositive If two angles are not congruent then the angles are not a vertical pair.
truth value true.
counter example __________________________________________________________
4. If Jerrod is in 11th grade, then Jerrod is in high school.
converse – If Jerrod is in high school, then he is in the 11th grade.
truth value false
counterexample Could be in the 9th, 10th, or 11th grade.
inverse - If Jerrod is in high school, then he is in the 11th grade.
truth value false
counterexample Could be in the 9th, 10th, or 11th grade.
contrapositive If Jerrod is in high school, then he is in the 11th grade
truth value true
counterexample ___________________________________________________________
Matching: Refer to the figure on the right for #5 – 7.
5.) __A____ Linear pair
A) 4 & 5
6.) ___C___ Complementary angles
B) 3 & 5
7.) ___B___ Vertical angles
C) 1 & 2
Name the property that justifies each statement.
8. mABC = mDEF and mDEF = mABC Symmetric
9. AB = CD, CD = EF. Therefore, AB = EF. Transitive
10. If x + 7 = 10, then x = 3. Subtraction
11. If AB + 12 = 25, then 12 = 25 – AB. Subtraction
12.. A  A Reflexive
13. Reasoning Use the diagram at the right to complete
the proof below.
Statements
B
LACB & LBCE supplementary
A. mLACB + mLBCE = 180
B. 5x + 9x + 40 = 180
C. 14x + 40 = 180
D. 14x = 140
E. x = 10
F. mLBCE = 9(10) + 40 = 130
G. LBCE  ACD
H. mLACD = 130
Reasons
Given
A. Definition of Supplementary
B. Substitution
C. Combine like terms
D. Subtraction
E. Division Property of Equality
F. Substitution Property
G. Vertical Angles are =
H. Substitution Property
14. Find the value of x.
15. Use your work from #14 to complete a
two-column proof with statements
and reasons for each step.
D
E
5x
4x
A
B
C
<ABE + <EBD = 90
Definition Complementary
4x + 5x = 90
9x = 90
X = 10
Substitution
Combine like terms
Division
16.
a) Write an equation and solve for x.
b) Find the measure of each angle.
mAEB  _______
mBEC  _______
mCED  _______
mAED  _______
17. Use your work from #16 to complete a two- column proof with statements and
reasons for each step.
< BEA = <CED
3x + 60 = 5x – 6
60 = 2x – 6
66 = 2x
33 = x
Vertical Angles are congruent
Substitution
Subtraction
Addition
Division