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Honors Geometry
Chapter 2 Test Review
Name: _____________________________________
1. What is the truth value of the statement A triangle has 2 congruent sides or a square has 2 sets of parallel sides?
2. Suppose p, q, and r are all true. What is the truth value of (~p ∧ q) ∨ r?
3. In a class of 58 students, 19 like watching soccer, 21 like watching hockey, and 5 like watching both. Make a Venn diagram of
these data. How many of these students do not like to watch either soccer or hockey?
4. Write the statement All chickens have two wings in if-then form.
5. Write the contrapositive of the statement If two lines are parallel to a third line, then they are parallel to each other.
6. Write a valid conclusion that follows from statements (1) and (2).
(1) If a football team wins the Big 10 championship, then they will play in the Rose Bowl.
(2) Ohio State wins the Big 10 championship.
7. Write a valid conclusion that follows from statements (1) and (2).
(1) If today is Thursday, then Amy is off from work.
(2) If Amy is off from work, then she will go to gym to workout.
8. Given:
Find:
AB  BC
B
ABO  (2 x  y ), OBC  (6 x  8),
AOB  (23 y  90), BOC  (4 x  4),
mABO
A
O
C
For numbers 9 & 10, complete the proofs below by supplying the reasons for each location.
x
 1  4
3
Prove: x = –15
9. Given:
Statements
Reasons
x
 1  4
3
x
2.  1  1  4  1
3
x
3.  5
3
 x
4.   3   5 (3)
3
1. Given
5. x = –15
5. Substitution
1.
2. Subtraction Property
3. Substitution
4. _________________________________________________
10. Given: BD bisects ABC.
 and  are complementary.
 and  are complementary.
Prove:   
Statements
Reasons
1. BD bisects ABC
1. Given
2.  and  are complementary.
2. Given
3.  and  are complementary.
3. Given
4. 
4. _________________________________________________
5.   
5. _________________________________________________
11. Complete the truth table.
p
T
T
F
F
q
T
F
T
F
∽p
∽p ∧ q
12. Write a concluding statement for the chain of reasoning.
~a  ~c
~b  d
a  ~d
b  ~f
∽ (~p ∧ q)
For numbers 13 – 17, state the definition, property, postulate, or theorem that justifies each statement.
13. If X is the midpoint of ZW , then ZX  XW .
14. If AB = CD, then CD = AB.
15. If PQ = RS, then PQ + AB = RS + AB.
16. If AB  CD and CD  EF , then AB  EF .
17. If mA = mB, then A  B.
18. If the ratio of m1 to m2 is 5 to 4, find m2.
19. Find the measure of each numbered angle: m1 = (5x + 20)°, m = (3x + 80)°.
20. Name the operation that transforms 4x – 2 = 7x + 7 to 4x = 7x + 9, then find the value of x.
21. If mA = (5x – 12)°, mB = (2x + 18)°, A and C are supplementary, and B and C are supplementary, find the value of x.
22. Multiple Choice: Determine which statement follows logically from statements (1) and (2).
(1) If a triangle is equilateral, then it has three congruent sides.
(2) If all the sides of a triangle are congruent, then each of its angles measures 60°.
a) If a triangle is not equilateral, then it cannot have congruent angles.
b) A figure with three congruent sides is always an equilateral triangle.
c) If a triangle is not equilateral, then none of the angles equals 60°.
d) If a triangle is equilateral, then each of its angles measures 60°.
For numbers 23 – 25, find the measure of each numbered angle and name the theorem that justifies your work.
23.
24.
25.
m∠7 = (5x + 5)°
m∠8 = (x – 5)°
m∠5 = (5x)°,
m∠6 = (4x + 6)°
m∠7 = (10x)°
m∠8 = (12x – 12)°
m∠11 = (11x)°
m∠13 = (10x + 12)°
For numbers 26- 28, complete the proofs below by supplying the reasons for each location.
26. Given: PR  QS
Prove: PQ  RS
Statements
Reasons
1. PR  QS
1. _________________________________________________
2. PR = QS
2. _________________________________________________
3. PQ + QR = PR
3. _________________________________________________
4. ________________________________
4. Segment Addition Postulate
5. PQ + QR = QR + RS
5. _________________________________________________
6. ________________________________
6. Subtraction Property
7. ________________________________
7. Definition of congruence of segments
27. Given: AB  BC
1 and 3 are complementary
Prove: 2  3
Statements
Reasons
1. AB  BC
1. _________________________________________________
2. ________________________________
2. Definition of perpendicular
3. mABC = 90°
3. Definition of right angle
4. mABC =m1 + m2
4. _________________________________________________
5. 90° = m1 + m2
5. Substitution
6. 1 and 2 are complementary
6. _________________________________________________
7. ________________________________
7. Given
8. 2  3
8. _________________________________________________
28. Given: 1 and 2 form a linear pair
m1 + m3 = 180°
Prove: 2  3
Statements
Reasons
1. 1 and 2 form a linear pair.
1. Given
2. m1 + m3 = 180°
2. Given
3. ________________________________
3. Supplementary Theorem
4. 1 is supplementary to 3
4. ________________________________________________
5. ________________________________
5. Congruent Supplements Theorem