Download ExamView - Geo REVIEW mdtrm 14

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Period____________________
Review for Geometry Midterm 2015: Chapters 1-5
Short Answer
1. What is the length of AC ?
2. Tell whether a triangle can have sides with lengths 1, 2, and 3.
3. Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles due
west, then changes direction and walks for 5 miles to point C. Dana hikes 6 miles due east, then changes direction
and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp.
6. What is the slope of the line shown?
4. Given: ∆ABC ≅ ∆MNO
Identify all pairs of congruent corresponding parts.
5. Apply the transformation M to the triangle with the
given vertices.
Identify and describe the transformation.
M: (x, y) → (x – 6, y + 2)
E(3, 0), F(1, –2), G(5, –4)
1
Name: ________________________
ID: A
7. What is the value of x? Identify the missing justifications.
m∠PQR = x − 11, m∠SQR = x + 1, and m∠PQS = 100.
m∠PQR + m∠SQR = m∠PQS
x – 11 + x + 1 = 100
2x – 10 = 100
2x = 110
x = 55
a. __________
b. Substitution Property
c. Simplify
d. __________
e. Division Property of Equality
8. Is the line through points P(–8, –1) and Q(–5, 8) parallel to the line through points R(3, 0) and S(1, –4)? Explain.
9. Compare m∠ABC and m∠CBD.
10. Where is the circumcenter of any given triangle?
11. Find the coordinates of the midpoint of the segment
whose endpoints are H(10, 1) and K(8, 3).
2
Name: ________________________
ID: A
12. What is the missing reason in the two-column proof?


→

→
Given: QS bisects ∠TQR and SQ bisects ∠TSR
Prove: ∆TQS ≅ ∆RQS
Statements
Reasons


→
1. QS bisects ∠TQR
2. ∠TQS ≅ ∠RQS
3. QS ≅ QS
1. Given
2. Definition of angle bisector
3. Reflexive property

→
4. SQ bisects ∠TSR
5. ∠TSQ ≅ ∠RSQ
6. ∆TQS ≅ ∆RQS
4. Given
5. Definition of angle bisector
6. ?
13. What is the value of x?
15. Write an equation in slope-intercept form of the
line through point P(1, 4) with slope –3.
16. Complete the two-column proof.
Given:
x
+ 9 = 11
5
Prove: x = 10
x
+ 9 = 11
5
x
=2
5
14. Find the value of x for which l is parallel to m. The
diagram is not to scale.
x = 10
3
a. ________
b. ________
c. ________
Name: ________________________
ID: A
18. ∠NPM ≅
17. Find the value of x. The diagram is not to scale.
?
19. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles.
Given: AB ≅ ED , BC ≅ DC , AC ≅ EC , ∠A ≅ ∠E
Prove: ∆ABC ≅ ∆EDC
Complete the proof.
Proof:
Statements
1. AB ≅ ED , BC ≅ DC , AC ≅ EC
2. ∠A ≅ ∠E
3. ∠BCA ≅ ∠DCE
4. ∠B ≅ ∠D
5. [3]
Reasons
1. Given
2. Given
3. [1]
4. [2]
5. Definition of congruent triangles
4
Name: ________________________
ID: A
20. Given: P is the midpoint of TQ and RS .
Prove: ∆TPR ≅ ∆QPS
Complete the proof.
Proof:
Statements
1. P is the midpoint of TQ and RS .
2. [1]
2. TP ≅ QP , RP ≅ SP
3. [2]
4. ∆TPR ≅ ∆QPS
21. Determine whether triangles
are congruent.
Reasons
1. Given
3. Vertical Angles Theorem
4. [3]
EFG and
23. Find m∠K .
PQR
24. If EF = 8x + 13, FG = 16, and EG = 85 , find the
value of x. The drawing is not to scale.
22. If Z is the midpoint of RT , what are x, RZ, and RT?
5
Name: ________________________
ID: A
25. The diagram shows the approximate distances from
Houston to Dallas and from Austin to Dallas. What
is the range of distances, d, from Austin to
Houston?
Use the diagram to find the following.
26. What are the measures of ∠ABD and ∠ABC ?
Classify each angle as acute, right, obtuse, or
straight.
28. Identify a pair of alternate exterior angles.
29. Find the value of x. The diagram is not to scale.
30. What additional information do you need to prove
∆ABC ≅ ∆ADC by the SAS Postulate?
27. Find the value of x. The diagram is not to scale.
6
Name: ________________________
ID: A
36. Justify the last two steps of the proof.
Given: PQ ≅ SR and PR ≅ SQ
Prove: ∆PQR ≅ ∆SRQ
31. In ∆ACE, G is the centroid and BE = 15. Find BG
and GE.
Proof:
1. PQ ≅ SR
32. Write the sides of ∆IJK in order from shortest to
longest.
2. PR ≅ SQ
3. QR ≅ RQ
4. ∆PQR ≅ ∆SRQ
1. Given
2. Given
3. ?
4. ?
37. Supplementary angles are two angles whose
measures have a sum of ____.
Complementary angles are two angles whose
measures have a sum of ____.
33. Tell whether a triangle can have sides with lengths
5, 11, and 7.
38. The legs of an isosceles triangle have lengths
3x + 2 and −x + 26. The base has length 2x + 2.
What is the length of the base?


→
34. MO bisects ∠LMN, m∠LMO = 8x − 28, and
m∠NMO = 2x + 38. Solve for x and find m∠LMN.
The diagram is not to scale.
39. For these triangles, select the triangle congruence
statement and the postulate or theorem that
supports it.
35. The lengths of two sides of a triangle are 3 inches
and 8 inches. Find the range of possible lengths for
the third side, s.
7
Name: ________________________
ID: A
40. ∆ABC is an isosceles triangle. AB is the longest
side with length 10x + 3. BC = 5x + 5 and CA =
4x + 11. Find AB.
41. Name the line and plane shown in the diagram.
42. What are the names of four coplanar points?
43. Find the value of x.
8
Name: ________________________
ID: A
45. Find the value of k. The diagram is not to scale.
44. Name the angle included by the sides MP and PN .
Multiple Choice
Identify the choice that best completes the statement or answers the question.
46. Write an equation in point-slope form & slope- intercept form of the line through point J(10, –2) with slope 7.
c. y − 2 = 7 (x + 10 )
a. y + 2 = 7 (x + 10 )
b. y + 2 = 7 (x − 10 )
d. y + 2 = −7 (x − 10 )
47. Which two lines are parallel?
5y = 4x − 5
I.
7y = 5 − 5x
II.
III. 7y + 5x = −1
a.
b.
I and III
I and II
c.
d.
II and III
No, two of the lines are parallel.
48. Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. I only
b. III only
c. I or III only
9
d.
I, II, or II
Name: ________________________
ID: A
49. Supply the missing reasons to complete the proof.
Given: ∠A ≅ ∠D and AC ≅ DC
Prove: BC ≅ EC
Statement
1. ∠A ≅ ∠D and
Reasons
1. Given
AC ≅ DC
2. ∠BCA ≅ ∠ECD
2. Vertical angles are congruent.
3. ∆BCA ≅ ∆ECD
3.
?
4. BC ≅ EC
4.
?
a.
b.
ASA; Corresp. parts of ≅ ∆ are ≅.
ASA; Substitution
c.
d.
AAS; Corresp. parts of ≅ ∆ are ≅.
SAS; Corresp. parts of ≅ ∆ are ≅.
50. Which statement can you conclude is true from the given information?
←

→
Given: AB is the perpendicular bisector of IK .
a.
b.
A is the midpoint of IK .
IJ = JK
c.
d.
AJ = BJ
∠IAJ is a right angle.
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ID: A
Review for Geometry Midterm 2015: Chapters 1-5
Answer Section
SHORT ANSWER
1. 8
2. No
3. Danny is farther from the base camp than Dana.
4. ∠A ≅ ∠M , ∠B ≅ ∠N , ∠C ≅ ∠O, AB ≅ MN , BC ≅ NO, AC ≅ MO
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
This is a translation 6 units left and 2 units up.
1
Angle Addition Postulate; Addition Property of Equality
No; the lines have unequal slopes.
m∠ABC > m∠CBD
the point of concurrency of the bisectors of the angles of the triangle
(9, 2)
ASA Postulate
68°
95
y = –3x + 7
a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
11
∠BCA
[1] Vertical Angles Theorem
[2] Third Angles Theorem
[3] ∆ABC ≅ ∆EDC
[1]. Definition of midpoint
[2] ∠TPR ≅ ∠QPS
[3] SAS
1
ID: A
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
The triangles are congruent because
x = 14, RZ = 88, and RT = 176
m∠K = 63°
x=7
40 < d < 440
m∠ABD = 16°; ∠ABD is acute.
m∠ABC = 180°; ∠ABC is straight.
56
∠2 and ∠6
58
∠ACB ≅ ∠ACD
BG = 5, GE = 10
32.
33.
34.
35.
36.
37.
38.
39.
40.
JK , IK , IJ
Yes
x = 11, m∠LMN = 120
5 < s < 11
Reflexive Property of ≅ ; SSS
180; 90
14
∆ABC ≅ ∆JKL, HL
AB = 63
EFG can be mapped to
←

→
41.
42.
43.
44.
45.
MN and plane M NP
Points D, A, B, and J are coplanar.
9
∠P
82
MULTIPLE CHOICE
46.
47.
48.
49.
50.
B
C
A
A
B
2
PQR by a reflection: (x,y) → (x,−y).