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Plane Geometry
Chapter 2 REVIEW
Name ___________________________
Hour _____ Date ________________
Circle the conjecture that is always true based upon the given information.
1. Given:
ABC and
EBD are vertical angles.
a.
ABC and
EBD form a linear pair
b.
ABC and
EBD are supplementary
c.
ABC and
EBD are complementary
d.
ABC and
EBD are congruent
2. Given: B is the midpoint of AC .
a. AB
b. AC + AB = BC
BC
3. Given: AC bisects
a. AB
4. Given:
BAD
AC
1 and
b. AB
Given:
a.
1 and
1 and
c.
AD
BAC
CAD
d.
BAD
CAD
2 are complementary
a. m 1 + m 2 = 90
5.
c. AB + AC = BC
b.
1+
2 = 90
c. m 1 + m 2 = 180
d.
1+
2 = 180
2 are supplementary
2 are a linear pair
c. m 1 and m 2 sum to 180
b.
1 and
2 are adjacent
d. m 1 and m 2 sum to 90
State a conjecture that is always true based upon each given. Give a REASON it is true.
6. Given: AB
7. Given:
BC
1
2
Conjecture: ________________________
Conjecture: ________________________
Reason:
Reason:
8. Given:
ABC
DBA (you make picture)
9. Given:
ABC
CBD (you make picture)
Conjecture: ________________________
Conjecture: ________________________
Reason:
Reason:
Determine if the conjecture is TRUE or FALSE based on the given information. Explain your answer.
10. Given: m 1 + m 2 =90
Conjecture: 1 and 2 form a right angle
11. Given: ABC and XYZ are right angles
Conjecture: ABC
XYZ
First, write each statement in if-then form. Second, circle the hypothesis and underline the conclusion.
Third, write the converse/inverse of the conditional. Fourth, Tell whether the converse/inverse is true or
false and explain.
12. If AB + BC = AC then B is between A and C.
Converse:
T or F
Explanation:
13. Angles that form a linear pair are adjacent.
Conditional:
Inverse:
T or F
Explanation:
14. Find the measure of each angle if m AHB= 2x + 10, m GHA = y + 38, m GHF = 2y + 7,
m DHE = 5x – 20, and AD CF .
m AHB = ______
C
m BHC = ______
m CHD = ______
B
H
m DHE = ______
D
A
m EHF = ______
E
G
F
m FHG = ______
m GHA = ______
m BHD = ______
m CHF = ______
15. Mark the figure based upon the given information.
A
a. AD
HC
b. HG bisects
B
AHF
G
c.
AFB
d. HA
BFC
H
DC
C
F
e. E is the midpoint of FD
E
D
16. If
AFC is a right angle; FB bisects
AFC; m AFB = 4x + 1, Find the measure of x.
Find the value of x and the measure of each angle.
17. m 1 = x2 + 6
m 2 = 14x – 2
2
1
18. Given:
Prove:
19. Given:
C is the midpoint of
Prove:
19. Given:
Prove:
20. Given:
Prove:
21. Given:
Prove:
ABC is a right angle
1 and 2 are complementary
22. Given: CB bisects AD
Prove: AB = BD
23. Given: CB bisects AD
Prove: 2AB = AD
24. Given: AB = CB, BG = BD
Prove: AD = CG
25. Given : AB = BE, BE = BG
Prove: AB = BG
26. Given: Picture
Prove: ABC and CBD are a linear pair
27. Given:
Prove:
1 and 2 are complementary,
2= 3
1 and
3 are complementary