Download Tree People Mid-Term Study Guide

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Tree People Mid-Term Study Guide
Multiple Choice
Identzfi the choice that best completes the statement or answers the question.
1. Find a counterexample to show that the conjecture is false.
Conjecture: Any number that is divisible by 5 is also divisible by 10.
a. 50
b. 25
c. 32
d. 40
2. Find a counterexample to show that the conjecture is false.
Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
a. 3 and5
b. 2 a n d 2
c. A counterexample exists, but it is not shown above.
d. There is no counterexample. The conjecture is true.
3. Identify the hypothesis and conclusion of this conditional statement:
If tomorrow is Monday, then yesterday was Saturday.
a. Hypothesis: Yesterday was Saturday. Conclusion: Tomorrow is Monday.
b. Hypothesis: Yesterday was not Saturday. Conclusion: Tomorrow is Monday.
c. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was not Saturday.
d. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Saturday.
- 4. Write this statement as a conditional in if-then form:
All triangles have three sides.
a. If a triangle has three sides, then all triangles have three sides.
b. If a figure has three sides, then it is not a triangle.
c. If a figure is a triangle, then all triangles have three sides.
d. If a figure is a triangle, then it has three sides.
- 5. Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
a. Sara Lucas lives in Springfield.
b. Jonah Lincoln lives in Springfield, Illinois.
c. Billy Jones lives in Chicago, Illinois.
d. Erin Naismith lives in Springfield, Massachusetts.
- 6. Another name for an if-then statement is a
-and the part following then is the -.
a. conditional; conclusion; hypothesis
b. hypothesis; conclusion; conditional
. Every conditional has two parts. The part following ifis the
c. conditional; hypothesis; conclusion
d, hypothesis; conditional; conclusion
Use the given property to complete the statement.
- 7. Transitive
- -Property
-of Congruence
-
ID: A
Name:
- 8. Substitution Property of Equality
If y = 6 and 6x + y = 14, then
a. 6 ( 6 ) - y = 14
b. 6 - y = 14
- 9.
.
c.
d.
6x+6 = 14
6 ~ - 6 =14
bisects LABC. mLABC = 9x. mLABD = 4x + 40. Find mLDBC.
a. 80
b. 360
c. 120
d.
280
d.
LAOE
10. Name an angle supplementary to LCOD.
a.
LBOD
b.
LDOE
c.
LCOB
- 1 1 . What can you conclude from the information in the diagram?
2. LCFE is a right angle
3. LCEFand ,&EF are adjacent angles
b. 1 . A B g C B
2. LCFE is a right angle
3. LCEFand LDEF are vertical angles
c. 1 .A B z CB
2. EC E ED
3. LECDand LACB are vertical angles
d. 1 . A B z A C
3. LECD and LACB are adjacent angles
ID: A
Name:
12. In the figure shown, mLAED = 126. Which of the following statements is false?
a,
b.
c.
d.
Not drawn to scale
mLAEB = 54
mLBEC= 126
LDEC and LDEA are vertical angles.
LDEA and LAEB are adjacent angles.
- 13. Supplementary angles are two angles whose measures have s u m .
Complementary angles are two angles whose measures have sum -,
a. 90; 180
b. 90; 45
c. 180; 360
d.
180; 90
- 14. Two angles whose sides are opposite rays are called -angles. Two coplanar angles with a common side,
a common vertex, and no common interior points are called -angles.
a. vertical; adjacent
b, adjacent; vertical
c, vertical; supplementary
d, adjacent; complementary
- 15. LDFG and LJKL are complementary angles. mLDFG = x + 1, and mLJKL = x - 5. Find the measure of each
angle.
a. LDFG = 48, LJKL = 42
c. LDFG = 47, LJKL = 43
b. LDFG = 48, LJKL = 52
d. LDFG = 47, LJKL = 53
- 16. L1 and L2 are supplementary angles. mL1 = x - 13, and mL2 = x + 63. Find the measure of each angle.
c. L1 = 52, L2 = 138
a. L1 = 65, L2 = 115
b. L 1 = 52, L2 = 128
d. L1 = 65, L2 = 125
ID: A
Name:
17. Complete the paragraph proof.
Given: LA and L B are right angles.
Prove: LA z L B
By the definition o f , mLA = 90 and mLB = 90. By the
mLA z mLB.
a, complementary angles; Substitution
b. right angles; Substitution
c, complementary angles; Reflexive
d. right angles; Symmetric
18. Find the value of x.
Drawing not to scale
a.
111
b.
19. Find the values of x andy.
Drawing not to scale
15
Property, mLA = mLB, or
ID: A
Name:
20. Which angles are corresponding angles?
a.
b.
L1 and L9
L2andL1
c. L5andL1
d, none of these
- 21. Which statement is true?
a.
b.
c.
d.
LCBE and LBEG are same-side angles.
LABH and LCBE are alternate interior angles.
LCBE and LBEG are alternate interior angles.
LABHand LCBE are same-side angles.
ID: A
Name:
22. Which is a correct two-column proof?
Given: r 11 s
Prove: L b and L h are supplementary.
\
a.
Statements
I R e asons
1. rlls
1. Given
2. L b E LC
2. Vertical Angles
3 . LCand L e are supplementary.
3. Same-Side Interior Angles
4. L e E L h
4. Vertical Angles
5. L b and L h are supplementary. 5. Substitution
b.
Statements
I R e asons
1. v (1s
1. Given
2. L b E L h
2. Corresponding Angles
3 . LCand L e are supplementary.
3. Same-Side Exterior Angles
4. L e E L h
4. Vertical Angles
5. LCand L h are supplementary. 5. Substitution
C.
Statements
I R e asons
1. Given
2. Vertical Angles
3 . L d and L h are supplementary.
3. Alternate Interior Angles
4. L e E L h
4. Vertical Angles
5. L b and L h are supplementary. 5. Same-Side Interior Angles
d. none of these
ID: A
Name:
23. Line r is parallel to line t. Find mL5. The diagram is not to scale.
\
- 24. Find the value of the variable if m
11 I, mL1= 2x + 42 and mL5 = 4x + 18. The diagram is not to scale.
- 25. Find the values of x and y. The diagram is not to scale.
- 26. Complete the statement. If a transversal intersects two parallel lines, then -,
a, corresponding angles are supplementary
b. same-side interior angles are complementary
c, alternate interior angles are congruent
d, none of these
- 27. Complete the statement. If a transversal intersects two parallel lines, then -angles are supplementary.
a, acute
c, same-side interior
b. alternate interior
d. corresponding
ID: A
Name:
28. Which is a correct two-column proof?
Given: LH and LY are supplementary.
Prove: L 11 N
a.
I Reasons
Statements
LH and LX are supplementary.
Given
LHzLE
Vertical Angles
L E and LX are supplementary.
Substitution
L
11 N
Same-Side Interior Angles Converse
b.
I Reasons
Statements
L H and LX are supplementary.
Given
L H z LE
Alternate Exterior Angles
L G and L Z are supplementary.
L
11 N
C.
Statements
I
Substitution
Same-Side Interior Angles Converse
I Reasons
LH and LX are supplementary.
Given
LHzLE
Vertical Angles
LE and LX are supplementary.
Same-Side Interior Angles
L 11 N
d. none of these
Same-Side Interior Angles Converse
ID: A
Name:
29. Which lines, if any, can you conclude are parallel given that mL1 + mL2 = 180? Justify your conclusion
with a theorem or postulate.
a, j
b, j
c, g
d. g
11 k, by the Converse of the Same-Side Interior Angles Theorem
11 k, by the Converse of the Alternate Interior Angles Theorem
11 h, by the Converse of the Alternate Interior Angles Theorem
11 h , by the Converse of the Same-Side Interior Angles Theorem
- 30. If BCDE is congruent to OPQR, then DE is congruent to
a. OR
b.
C.
QR
?
.
d.
OP
- 3 1. In the paper airplane, ABCD E EFGH, mLB = mLBCD = 90, and mLBAD = 159. Find mLGHE.
B
C
G
Drawing not to scale
F
- 32. If ASTU E AKLM, which of the following
- can you NOT conclude as being true?
- a. L T E LL
b. TU E LM
c. L S s L K
d. ST z KM
ID: A
Name:
a.
LCBA
b.
LACB
c.
LABC
d.
LCAB
34. The two triangles are congruent as suggested by their appearance. Find the value o f f . The diagrams are not
to scale.
- 35. Given AABC z APQR, mLB = 4v + 2, and mLQ = 5v - 4, find mLB and mLQ.
a. 26
b. 27
c. 34
d. 37
ID: A
Name:
36. Justify the
the proof,
-last-two steps
-of Given: PQ G SR and PR z SQ
Prove: APQR z ASRQ
S
Proof:
- 1. P Q z SR
- 2. PR z SQ
- -
1. Given
2. Given
3,QRzRQ
4.APQRg ASRQ
3.
4.
a.
b.
?
?
Symmetric Property of E ; SSS
Reflexive Property of z; SAS
c.
d.
Reflexive Property of z; SSS
Symmetric Property of z; SAS
- 37. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
B
C
D
a. L C B Az LCDA
b. AC E BD
c.
d.
L
B A Cz LDAC
AC 1BD
ID: A
Name:
- 38. State whether AABC and AAED are congruent. Justify your answer.
a.
b,
c.
d.
yes, by either SSS or SAS
yes,bySSSonly
yes, by SAS only
No; there is not enough information to conclude that the triangles are congruent.
- 39. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
a.
c.
ID: A
Name:
40. What is the missing reason in the two-column proof?
-----t
-----f
Given: AC bisects LDAB and CA bisects LDCB
Prove: ADAC AABC
=
Statements
Reasons
1.
bisects LDAB
2. LDAC E LBAC
3.AC z AC
1. Given
2. Definition of angle bisector
3. Reflexive property
4.
bisects LDCB
5. LDAC E LBCA
6 , ADAC E ABAC
4. Given
5. Definition of angle bisector
6. J
-
a.
b.
AAS Theorem
SSS Postulate
c.
d.
SAS Postulate
ASA Postulate
- 41. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
a. either ASA or AAS
b. ASA only
c. AAS only
d, neither
ID: A
Name:
42. Find the value of x. The diagram is not to scale.
43. Points B, D, and F are midpoints of the sides of AACE. EC = 35 and DF = 23. Find AC. The diagram is not to
scale.
A
a.
11.5
- 44. Find the value of x.
b.
70
ID: A
Name:
45. Find the center of the circle that you can circumscribe about the triangle.
A
46. Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
11. on the triangle
111, outside the triangle
a. I only
b. I1 only
c. I or I1 only
d. I, 11, or I1
- 47. Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
11. on the triangle
111, outside the triangle
a. I only
b.
I11 only
c.
I or I11 only
- 48. In AABC, G is the centroid and BE = 21. Find BG and GE.
d.
I, 11, or I1