Geometry Midterm Exam Review
2010-2011
Name___________________________________________________________
Be familiar with the concepts and terms below.
Exam covers Chapters 1 – 5 & Constructions
Formulas: Know the formula for each and know when to use each formula.
•pythagorean theorem
•distance formula
•midpoint formula
•slope between 2 points
•slope-intercept form of a linear equation
Chapter 1: Intro to geometry
•basic geometry notation
•collinear
•ruler postulate
•angle addition postulate
•individual angles
acute, obtuse, right, straight
Chapter 2: Reasoning
•make conjectures
•converse, inverse, contrapositive
•properties of algebra
Chapter 3: Perpendicular & Parallel Lines
•transversal
•alt. int. angles
•corresponding angles
•proving lines are parallel
•points, lines, planes
•perpendicular vs parallel
•segment addition postulate
•bisect
•special pairs of angles
adjacent, vertical, complementary,
supplementary, linear pair
•conditional statements
•laws of logic - detachment vs syllogism
•Venn Diagrams
•parallel, perpendicular, skew
•alt. ext. angles
•consecutive int. angles
Chapter 4: Identifying Congruent Triangles
•classify triangles - acute, right, obtuse, scalene, isosceles, equilateral
•ext. angle theorem
•prove 2 ∆’s are congruent
•SSS, ASA, SAS, AAS
•CPCTC
Chapter 5: Triangle Inequalitities
•prove 2 rt. ∆’s are : LL, LA, HL, HA
•arrange sides or  from smallest to greatest
•determine if the given sides can form a ∆
•∆ inequality - SAS ineq., SSS ineq.
1
Geometry Midterm Exam Review
2010-2011
1. Choose the statement that best describes the Venn Diagram.
a.
All football players are athletes.
b.
Some football players are athletes.
c.
Athletes are not football players.
d.
All athletes are football players.
2. What is the converse of the statement “If an angle is a right angle, then it is equal to 90˚ ?”
3. Given the statement “If I win, then you lose.”, how is the statement “If I don’t win, then you don’t lose.” related to
it?
4. Given the statement “If it snows, then we don’t go to school.”, how is the statement “If we go to school, then it did
not snow.” related to it?
5. What is the contrapositive of the statement p
~q?
6. According to the diagram, which of the following is true?
a.
All parallelograms are either rectangles or rhombi.
b.
All parallelograms are both rectangles and rhombi.
c.
No parallelogram is both a rectangle and a rhombus.
d.
Some parallelograms are both a rectangle and a rhombus.
7. According to the diagram, which of the following is true?
a.
All polygons are pentagons.
b.
Polygons are not pentagons.
c.
All pentagons are polygons.
d.
Some pentagons are polygons.
8. Apply the Law of Syllogism to the following two sentences and make a conclusion
If I recycle my newspapers, then I contribute to saving a tree.
If I contribute to saving a tree, then I helped improve the quality of our air.
9. Given that M is the midpoint of segment XY , with X(-1, 2) and Y(6, -2), find the coordinates of M.
10. What is the slope of the line through (1, -8) and (5, 6)?
11. Given the points A(-12, 7) and B(1 ,1), find the distance from A to B.
2
Geometry Midterm Exam Review
2010-2011
12. Find the distance from Z to L on the number line shown.
a. 13
13. If
1 and
b. -14
c. 14
d. -12
2 are complementary angles, and the m 1= 39˚, then find m 2 .
14. If m ABD = 132°, then m DBC = ____.
15. If m ABD = 6x + 3 and m DBC = 2x - 7, then m ABD = ____.
16. If m EGH = 120° and m EGF = 54°, then m FGH = ____.
17. A is five times the size of its complement ( B). What is the measure of each angle?
m A = _____, m B =______
18. If m 1 = 46° and m 3 = 42°, then m 2 = ____.
19. If m 1 = 2x + 10 and m 3 = 3x , then m 1 = _____
Use the figure below to answer the following question(s). j || k and m || n
20. What is the relationship between 9 and 11?
a. alternate interior
b. alternate exterior
c. corresponding
d. same side interior (consecutive int)
21. If
5 = 112°, what is the m 10?
22. If m 3 = 69°, what is the m 16?
23. If m 10 = 8x - 40 and m 11 = 2x + 20, what is x?
3
Geometry Midterm Exam Review
2010-2011
Use the figure below to answer the following question(s).
24. Line a is parallel to line b if...
a.
m 1 = m 4 b.
c.
m 5 = m 3 d.
m 3=m 8
m 3=m 6
25. What would be the value of x so a || b given m 4 = 6x + 11 and m 6 = 4x-1?
26. Find the slope of any line parallel to the line passing through M(3,3) and N(5,7).
27.
28. Given that
needed to prove
ABC
, name the missing piece of information
ADC using the SAS method.
29. Given:
, name the missing piece of
information needed to prove ABC
CDA using the SSS method.
30. Jan is making a triangular garden with railroad posts. She has two posts that are 8 ft and 12 feet. Which of the
following post lengths are not possible?
a. 8 ft
b. 4 ft.
c. 19 ft
d. 11 ft.
31. On a map, Richmond, Charlottesville, and Fredericksburg form a triangle. Richmond is 70 miles from
Charlottesville and Fredericksburg is 60 miles from Richmond. Which is a possible distance between Fredericksburg
and Charlottesville?
a. 10 miles
b. 80 miles
c. 130 miles d. 200 miles
4
Geometry Midterm Exam Review
2010-2011
32. From longest to shortest, the sides of ∆ABC are . . .
33. From smallest to greatest, the angles of ∆ABC are . . .
34. What is m 2?
35. The figure has angles measures as shown.
What is the measure of BCD?
36. What is the inverse of the statement “If an angle is obtuse, then it is not equal to 90°”.
37. Given the statement “If you stay, then I’ll go”, how is the statement “If I go, then you’ll stay” related to it?
38. What is the contrapositive of the statement p
q?
39. Forty-eight girls are enrolled in classes at a dance studio.
Use the Venn Diagram to determine how may girls are
taking both Ballet and Tap dance classes.
40. Use the Law of Syllogism to determine the conclusion for the following statement:
If a throat culture test is positive, then the doctor will prescribe antibiotics.
If the doctor prescribes antibiotics, then the patient will visit the pharmacy.
5
Geometry Midterm Exam Review
2010-2011
41. Given that M is the midpoint of AB, with A(-9,4) and B(3,-2), find the coordinates of M.
42. Find the slope of the line perpendicular to the line which contains the points C(-1, 8) and D(2, 6).
43. Given the points E(4, -6) and F(-3 ,-5), find the length of EF.
44.
PQR is isosceles with its vertex angle at  Q. If PQ = 3x, QR = 4x-7 and PR = 5x+4, find the length of PR .
45. The vertex angle of an isosceles triangle is 38  , what is the measure of the base angles?
11
B
ABC  DEF
46. Solve for the values of x and y so that
C
E
5x+2
A
4y-1
F
8x-13
D
47. The measures of the angles of a triangle are 38  , 47  and 5x  . Find x.
48. What would be the value of x so a || b with
m 1 = 6x + 11 and m 8 = 14x-109?
17
S
49. Write an inequality:
T
42
RS _____ TM
44
R
50. Write an inequality.
M
17
E
9
m 1 _____ m 2
D
1 55
55
2
9
A
11
B
13
C
51. Between what two numbers would the 3rd side of a triangle have to be given that two of its sides are 18 cm and 32
cm?
52. Which set of numbers would be impossible to use to form a triangle?
a. 8, 16, 7
b. 13, 20, 17 c. 5, 5, 5
d. 12, 20, 12
6