Geometry CP Midterm Exam Review 2014

Name______Teacher______

Review Packet:

  1. The format of the review packet is not the format of the exam.
  2. Please refer back to previous notes, homework, and class examples for more practice.
  3. Complete the packet to the best of your ability on your own, then bring your remaining questions to your teacher(s).

Exam Helpful Hints:

  1. Read directions very carefully.
  2. When necessary, draw a diagram!
  3. Use the choices of multiple choice questions.

Exam Info:

  1. Format: The exam will include multiple choice as well as open-ended questions.
  2. Students will be allowed to use calculators (graphing calculators will be required to clear all memory!) You MUST bring your own! You will not be provided with one.
  3. If you are found with any materials regarding this exam, or in your calculator, you will fail the exam with a ZERO.
  4. No Cell phones are permitted in the exam area. Leave them at home or in your lockers.

Vocabulary: You are responsible for the following terms, theorems and postulates.

collinear Points
coplanar Points
ray
plane
line
line Segment
segment addition postulate
segement subtraction postulate
midpoint
bisect
acute angle
right angle
obtuse angle
straight angle
angle bisector
complementary angles / Parallel Lines
Perpendicular Lines
Skew Lines
Parallel Planes
Perpendicular Planes
Corresponding angles
a. Postulate
b. Converse
Alternate interior angles
a. Theorem
b. Converse
Alternate exterior angles
a. Theorem
b. Converse
Consecutive interior angles
a. Theorem
b. Converse / Right Triangle
Scalene Triangle
Equilateral Triangle
Equiangular Triangle
Acute Triangle
Isosceles Triangle
Obtuse Triangle
Exterior Angle Theorem
Base Angles Theorem
  1. Converse
Hinge Theorem
  1. Converse
Triangle Inequality Theorem
Perimeter
Area of Triangle
Midsegment
supplementary angles
adjacent angles
linear pair
vertical angles
linear pair postulate
vertical angle theorem
polygon
equilateral
equiangular
regular polygon
concave polygon
convex polygon
interior angles
exterior angles
conditional
converse
inverse
contrapositive / Triangle Congruence Postulates:
SSS
SAS
HL
ASA
AAS /
  1. Theorem
Perpendicular Bisector
Median
Altitude

Points, lines and planes

For questions 1-9, use the diagram to determine if the statement is true or false.

  1. and are parallel
  2. andare perpendicular
  3. and are skew
  4. , , and are collinear
  5. , , and are collinear
  6. , J, , and are coplanar
  7. , G, and are coplanar
  8. is between and
  9. There are no parallel planes in this diagram.

Angles

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Geometry CP Midterm Exam Review 2014

  1. Use the diagram. Find the value of and m∢1.
  2. Use the diagram. bisects ∢, ∢ = and ∢ = 19. Find thevalue of , and the ∢.

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

  1. Two angles are supplementary. One angle is 5 less than 4 times the other. Find the measure of each angle.
  2. Two angles are complementary. One angle is 4 times the other. Find the measure of the larger angle.

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Geometry CP Midterm Exam Review 2014

For questions 14-19, use the diagram. Given thatand, identify each of the following.

  1. A right angle
  2. Two congruent supplementary angles
  3. Two non-congruent supplementary angles
  4. Two adjacent complementary angles
  5. A pair of vertical angles
  6. A midpoint
  1. In the figure below bisects ∢ and bisects ∢.
    ∢ = , ∢ =

a)Solve for .

b)Determine the measure of∢.

Segment and Line Properties

  1. is a point between and . = , = , and = .
    a) What is the length of?

b) Is the midpoint of ?

  1. H is the midpoint of. = and = .Find the length of and .
  1. In the diagram, is the midpoint of and is the midpoint of .
    = =

a) Solve for .

b) What is the length of ?

  1. What is the midpoint of the segment that connects the points and
  1. is the midpoint of segment .Given and , find the coordinates of endpoint .
  1. What is the slope of a line that is parallel to a line with slope?
  1. What is the slope of a line that is perpendicular to a line that has a slope ?

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Geometry CP Midterm Exam Review 2014

Parallel Lines

For questions 28-34, use the diagram to determine which lines, if any, are parallel based on the given statement.

  1. ∢≌∢
  2. ∢ is supplementary to ∢
  3. ∢≌∢
  4. ∢≌∢
  5. ∢ is supplementary to ∢
  6. ∢≌∢
  7. ∢≌∢

For questions 35-39, use the diagram which shows two sets of parallel lines.

  1. If m∢1 = 100°, find m∢14.
  2. If m∢9 = 120°, find m∢6.
  3. If m∢2 = 62°, find m∢12.

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Geometry CP Midterm Exam Review 2014

  1. If ∢7 = (5 + 8)°, ∢14 = (12 + 2)°, solve for .
  2. If ∢6 = (8 + 5)°, ∢10 = (10 7)°, solve for .

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Geometry CP Midterm Exam Review 2014

Logic

For questions 42-46, use the conditional statement “If two angles are vertical, then they are congruent.”

  1. Write the converse: ______
  2. Write the inverse: ______
  3. Write the contrapositive: ______
  4. Can this be written as a biconditional statement? ______
  5. Since the conditional statement is true, which other statement is also true? ______

Triangles

  1. The exterior angle at the base of an isosceles triangle measures 130°. Find the measure of the vertex angle.
  1. In ∆, ∢°, ∢° and . Find .
  1. The three angles of a triangle are , and Find the value of the smallest angle.
  1. ∆ is isosceles with ∢≌∢. If , and Find the length of the base.
  1. In ∆, ∢° and ∢B °. What is the largest side of the triangle?
  1. In equilateral ∆, point is the midpoint of , and point is the midpoint of . If , what is the perimeter of ∆.
  1. In ∆, ∢ is more than ∢ and ∢ is more than ∢. What is the measure of each angle?
  1. If a triangle has sides length 5 and 8, what are the possibilities for the length of the third side?

For questions 53-56, use the diagram.

  1. ∢1 = 40°, ∢2 = 110°, ∢5 = ______°
  2. ∢1 = 55°, ∢2 = 95°, ∢6 = ______°
  3. ∢4 = 118°, ∢1 = (2 + 8)°, ∢3 = ( + 5)°. = ______
  1. ∢1 = (3 +12)°, ∢2 = (2 + 14)°, ∢3 = (8 15)°. = ______

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Geometry CP Midterm Exam Review 2014

For questions 57-61, use the diagram to determine which method, if any, proves the triangles congruent.

  1. is a median, ∢3 ≌∢4.
  2. ⊥ , ≌
  3. ∢3 ≌∢4, ∢A ≌∢C
  4. B is the midpoint of
  5. ∢1≌∢2, ≌

For questions 62-64, if possible name the theorem/postulate that proves the triangles are congruent.

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

For questions 65 and 66, write a complete proof.

  1. Given: is the midpoint of

Prove:

  1. Given: bisects

bisects ∢

Prove:∢A ≌∢B

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Geometry CP Midterm Exam Review 2014

  1. Use the diagram to solve for and . Round to the nearest tenth.
  1. Use the diagram to solve for and .

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

For questions 69-80, determine if the statement is always, sometimes, or never true.

  1. If a triangle is isosceles it is also equilateral
  2. “AAA” is a rule used to prove two triangles congruent.
  3. If two angles are congruent, then they are vertical.
  4. Angles that form a linear pair are complementary
  5. In triangle ABC, if point D is the midpoint of , then is a median of the triangle.
  6. If alternate exterior angles are supplementary, then the lines are //.
  7. An equilateral triangle is isosceles.
  8. An acute triangle is right.
  9. An acute triangle is isosceles.
  10. A right triangle is scalene.
  11. An altitude of a triangle can be outside the triangle.
  12. An angle bisector of a triangle is also the median of the triangle.

Special Segments in Triangles.

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Geometry CP Midterm Exam Review 2014

  1. Use the following diagram to name each:


  1. Given are the midpoints of the sides of :

a)Find the value of .

b)Find the value of .

c)Find .

  1. Verify the Midsegment Theorem for in below.

a)Slope = ______

b)Slope = ______

c) = ______

d) = ______

e) Explain your conclusion using complete sentences:

______

______

  1. Is the triangle in question 83 equilateral?

Polygons

Identify if each shape is a polygon. If it is, state if it is convex or concave.

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

For questions 88-90, fill in the table.

Polygon / Sum of Interior Angles / Sum of Exterior Angles
Heptagon
Dodecagon
15-gon

For questions 91-93, fill in the table.

Regular Polygon / Each Interior Angle / Each Exterior Angle
Octagon
Decagon
20-gon

For questions 94-96, an interior angle measure is given. Name the regular polygon.

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Geometry CP Midterm Exam Review 2014

  1. 135°
  2. 170°
  3. 144°

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Geometry CP Midterm Exam Review 2014

For questions 97-99, an exterior angle measure is given. Name the regular polygon.

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Geometry CP Midterm Exam Review 2014

  1. 72°
  2. 5°
  3. 40°

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Geometry CP Midterm Exam Review 2014

  1. A pentagon has angle measures of°, °, and °. Find the measure of the largest angle.

Similar Triangles

  1. Given ∆~∆, with a scale factor of , if = 21, find .
  1. Given ∆~∆, find the value of .

For questions 103-106, solve for the variables in each diagram.

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Geometry CP Midterm Exam Review 2014

  1. is the angle bisector of ∢ABC

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Geometry CP Midterm Exam Review 2014

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Geometry CP Midterm Exam Review 2014

  1. is the angle bisector of ∢BAC

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Geometry CP Midterm Exam Review 2014

Answer Key:

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Geometry CP Midterm Exam Review 2014

  1. false
  2. false
  3. true
  4. true
  5. false
  6. false
  7. true
  8. true
  9. false
  10. x = 12.5

m∢1 = 127°

  1. x = 6
    m∢PAT = 50°
  2. m∢1 = 37°
    m∢2 = 143°
  3. m∢1 = 18°
    m∢2 = 72°
  4. multiple answers
  5. multiple answers
  6. multiple answers
  7. ∢ADF and ∢FDB OR
    ∢BXD and ∢DXA
  8. multiple answers
  9. D
  10. a) x = 9
    b) 8°
  11. a) = 21
    b) not a midpoint
  12. = 9
  13. a) x = 9.5
    b) = 70
  14. (2, 1)
  15. (8, 11)
  16. none
  17. none
  18. none
  19. 80°
  20. 60°
  21. 62°
  22. x = 10
  23. x = 6
  24. If two angles are congruent, then they are vertical.
  25. If two angles are not vertical then they are not congruent.
  26. If two angles are not congruent, then they are not vertical.
  27. No; the converse is not true.
  28. contrapositive
  29. 80°
  30. = 5cm
  31. 70°
  32. 78ft
  33. 48in
  34. m∢G = 56°
    m∢H = 76°
    m∢I = 48°
  35. 3 < x < 13
  36. 150°
  37. 30°
  38. x = 35
  39. x = 13
  40. SAS
  41. HL
  42. AAS
  43. NEI
  44. NEI
  45. AAS
  46. SAS
  47. NEI

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Geometry CP Midterm Exam Review 2014

Statements / Reasons
  1. C is the midpoint of , ,
/
  1. Given

/
  1. Definition of Midpoint

  1. ∢B ≅∢C
/
  1. Corresponding Angles Postulate

  1. ∆DAC ≅ ∆FCB
/
  1. SAS

/
  1. CPCTC

Statements / Reasons
  1. bisects,,
bisects ∢FDG /
  1. Given

/
  1. Definition of Bisect

  1. ∢FDB≅∢BDG
/
  1. Definition of Bisect

  1. ∢EDA ≅∢BDG
/
  1. Vertical Angle Theorem

  1. ∢FDB ≅∢EDA
/
  1. Transitive Property

  1. ∆EDA ≅∆FDB
/
  1. SAS

  1. ∢A ≅∢B
/
  1. CPCTC

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Geometry CP Midterm Exam Review 2014

  1. x = 25.7
    y = 22.9
  2. x = 7
    y = 16
  3. sometimes
  4. never
  5. sometimes
  6. never
  7. always
  8. sometimes
  9. always
  10. never
  11. sometimes
  12. sometimes
  13. always
  14. sometimes
  15. a)
    b)
    c) none
    d)
    e)
  16. a) x = 6
    b) y = 20
    c) = 17

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Geometry CP Midterm Exam Review 2014

  1. a)
    b) c)
    d)
    e) is a midsegment of ∆ABC because it is both parallel to and half the length of .
  2. not equilateral
  3. concave
  4. not a polygon
  5. convex

Polygon / Sum of Interior Angles / Sum of Exterior Angles
Heptagon / 900° / 360°
Dodecagon / 1800° / 360°
15-gon / 2340° / 360°
Regular Polygon / Each Interior Angle / Each Exterior Angle
Octagon / 135° / 45°
Decagon / 144° / 36°
20-gon / 162° / 18°
  1. octagon
  2. 36-gon
  3. decagon
  4. pentagon
  5. 72-gon
  6. nonagon
  7. 158°
  8. = 49
  9. x = 0.5
  10. x = 4
    y = 24
  11. x = 12
  12. x = 10
  13. x = 3

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