College Prep Geometry
MID-TERM STUDY GUIDE
Mrs. Miller
Name: __________________
Due: Thursday, January 9, 2014
To receive full credit you must have
• Tried EVERY PROBLEM
• Work shown for EVERY PROBLEM
• All work done in this packet
Name: ________________________ Class: ___________________ Date: __________
2013-2014 CP Geometry Midterm Exam Study Guide
Short Answer
Refer to Figure 1.
Figure 1
1. Name the intersection of lines m and n.
2. Name a line that contains point G.
3. Name the plane containing lines p and m.
4. What is another name for line p?
1
ID: A
Name: ________________________
ID: A
5. Name three points that are collinear.
Refer to Figure 2.
Figure 2
6. How many planes are shown in the figure?
7. Name the intersection of plane DAB and a plane that contains points E and B.
8. Name an intersection of plane DEF and the plane that contains points F and C.
2
Name: ________________________
ID: A
Refer to the figure below.
9. Name all segments parallel to AB.
10. Name all segments skew to GH .
11. Name all planes intersecting plane CBG.
Find the measurement of the segment.
12. PR = 16.3 mm, RS = 11.2 mm
PS = ?
3
Name: ________________________
ID: A
Use the number line to find the measure.
13. RH
Use the Distance Formula to find the distance between each pair of points.
14.
Find the coordinates of the midpoint of a segment having the given endpoints.
15. Q ÊÁË 11, 8 ˆ˜¯ , R ÊÁË 2, 11 ˆ˜¯
4
Name: ________________________
ID: A


→
In the figure, GK bisects ∠FGH .
16. If m∠FGK = 6v − 3 and m∠KGH = 3v + 6, find angle x.
17. The measures of two complementary angles are 8q − 5 and 8q + 15. Find the measures of the angles.
18. The measures of two supplemenatry are such that one angle is 30 more than the other. Find the measures of
the angles.
Make a conjecture about the next item in the sequence.
19. 1, − 8, − 17, − 26, − 35
5
Name: ________________________
ID: A
←
→
←
→
←

→
←

→
20. In the figure, m∠NML = 135, PQ Ä TU and KL Ä NM . Find the measure of angle TLR.
21. In the figure, AB Ä CD. Find x and y.
Write the statement in if-then form.
22. Two angles measuring180 are supplementary.
23. Identify the hypothesis of the statement Two angles are complementary if they have a sum of 90 degrees..
6
Name: ________________________
ID: A
24. Identify the conclusion of the statement Two angles are complementary if they have a sum of 90 degrees..
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
25. Given: m2 + 6 = 15
Conjecture: m = 3
26. Given: Two angles are adjacent.
Conjecture: They are both acute angles.
Use the figure to find the angles.
27. Name two acute vertical angles and two obtuse vertical angles.
Obtuse:
Acute:
Explain the difference between the two answers.
7
Name: ________________________
ID: A
28. Name a linear pair.
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem
that justifies your answer.
29. ∠2 ≅ ∠6
30. In the figure, p Ä q . Find m∠1.
8
Name: ________________________
ID: A
Determine the slope of the line that contains the given points.
31. T ÊÁË 3, 3 ˆ˜¯ , V ÊÁË 5, 8 ˆ˜¯
Write an equation in slope-intercept form of the line having the given slope and y-intercept.
32. m: −
2
, b: − 6
9
Write an equation in point-slope form of the line having the given slope that contains the given point.
33. m = −3, ÊÁË −2, 1 ˆ˜¯
Find each measure.
34. m∠1, m∠2, m∠3
9
Name: ________________________
ID: A
35. m∠1, m∠2, m∠3
Identify the congruent triangles in the figure.
36.
Name the congruent angles and sides for the pair of congruent triangles.
37. ∆GHK ≅ ∆XZT
10
Name: ________________________
ID: A
38. Triangle FJH is an equilateral triangle. Find x and y.
Refer to the figure. ∆ARM, ∆MAX, and ∆XFM are all isosceles triangles.
39. What is m∠RAM ?
40. What is m∠MAX ?
41. What is m∠ARM ?
11
Name: ________________________
ID: A
42. Which segment is the shortest possible distance from point D to plane P?
43. Determine the relationship between ∠CPV and ∠CTK
44. Name the shortest and longest side of
ABC.
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
45. 4, 6, 17
12
Name: ________________________
ID: A
Refer to the figure to determine which is a true statement for the given information.
46. KN is an altitude.
47. KN is a median.
48. NK is an angle bisector.
13
Name: ________________________
ID: A
49. AC is a perpendicular bisector and ∠B = 49°. Find the value of x, y, and the measure of ∠CAB. Put your
final answer on the appropriate line.
x = __________________
y = __________________
m∠CAB = _____________
14
Name: ________________________
ID: A
50. Write a two-column proof for the problem.
Given: AB ≅ ED
C is the midpoint of BD
∠B and ∠D are right angles
Prove:
ABC ≅
EDC
A
C
D
B
E
Statements
Reasons
15
KEYSTONE
Re f E FERENCE
GEOMETRY FORMULA SHEET ─ PAGE 1
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Properties of Circles
Right Triangle Formulas
Angle measure is represented by x. Arc measure is represented
by m and n. Lengths are given by a, b, c, and d.
Pythagorean Theorem:
Inscribed Angle
n°
x°
If a right triangle has legs with
measures a and b and hypotenuse
with measure c, then...
c
a
a2 + b2 = c2
b
1
x= n
2
Trigonometric Ratios:
x°
sin θ =
Tangent-Chord
n°
x=
1
n
2
hypotenuse
opposite
cos θ =
θ
adjacent
m°
a
c
x°
hypotenuse
adjacent
hypotenuse
tan θ =
2 Chords
d
opposite
opposite
adjacent
a·b=c·d
n°
x=
b
1
(m + n)
2
Coordinate Geometry Properties
a
x°
n°
Tangent-Secant
b
a 2 = b (b + c)
m°
x=
c
1
(m − n)
2
Distance Formula:
Midpoint:
Slope:
m°
x1 + x2
2
n° x°
b
b (a + b) = d (c + d )
d
c
x=
1
(m − n)
2
,
(x2 – x 1)2 + (y2 – y 1)2
y1 + y2
2
y2 − y1
m=
x2 − x1
2 Secants
a
d=
Point-Slope Formula:
(y − y 1) = m (x − x 1)
Slope Intercept Formula:
y = mx + b
Standard Equation of a Line:
2 Tangents
a
m°
n°
a=b
x°
b
Ax + By = C
x=
1
(m − n)
2
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.
KEYSTONE
Re f E FERENCE
GEOMETRY FORMULA SHEET ─ PAGE 2
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Plane Figure Formulas
Solid Figure Formulas
P = 4s
A=s · s
s
w
s
l
P = 2l + 2w
A = lw
w
SA = 4r 2
4
V = r 3
3
r
l
a
P = 2a + 2b
A = bh
h
h
b
SA = 2r 2 + 2rh
V = r 2h
r
a
c
d
h
P=a+b+c+d
1
A = 2 h (a + b)
SA = r 2 + r r 2 + h 2
1
V = r 2h
3
h
b
r
c
SA = 2lw + 2lh + 2wh
V = lwh
h
d
h
P=b+c+d
1
A = 2bh
b
SA = (Area of the base) +
1 (number of sides)(b)( )
2
h
b
base
r
C = 2r
A = r 2
V=
1
(Area of the base)(h)
3
b
Euler’s Formula for Polyhedra:
Sum of angle measures = 180(n – 2),
where n = number of sides
V−E+F=2
vertices minus edges plus faces = 2
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.