Geometry Enriched Midterm Review 2015
The following sections will be included on your midterm.
Chapter 1 – Tools of Geometry
1-1 – Points, lines, and Planes
1-2 – Linear Measure
1-3 – Distance and Midpoint
1-4 – Angle Measure
1-5 – Angle Relationships
Chapter 2 – Reasoning and Proof
2-1 – Inductive Reasoning ad Conjecture
2-2 - Logic
2-3 – Conditional Statements
2-4 - Deductive Reasoning
2-5 – Postulates
2-6 – Algebraic Proof
2-7 – Proving Segment Relationships
2-8 – Proving Angle Relationships
Chapter 3 – Parallel and Perpendicular Lines
3-1 – Parallel Lines and Transversals
3-2 – Angles and Parallel Lines
3-3 – Slopes of Lines
3-4 – Equations of lines
3-5 – Proving Lines Parallel
3-6 – Perpendiculars and Distance
Chapter 4 – Congruent Triangles
4-1 – Classifying Triangles
4-2 – Angles of Triangles Triangle
4-3 – Congruent Figures Triangle
4-4 – Congruence by SSS and SAS
4-5 – Congruence by ASA and AAS
4-6 – Isosceles and Equilateral Triangles
4-8 – Triangles and Coordinate Proofs
Chapter 5 – Relationships in Triangles
5-1 – Bisectors of Triangles
5-2 – Medians and Altitudes of Triangles
5-3 – Inequalities in One Triangle
5-4 – Indirect Proof
Please study from your old tests/quizzes along with doing this packet for review.
Your midterm consists of 2 sections; multiple choice and open-ended. This packet has a mixture of both types.
IMPORTANT: TO STUDY FOR THIS MIDTERM, YOU SHOULD LOOK OVER ALL MATERIAL
THAT HAS BEEN COVERED IN YOUR CLASS, SUCH AS HOMEWORK, ASSESSMENTS, AND
NOTES. DO NOT ONLY STUDY FROM THIS PACKET!!! PACKET IS DUE THE DAY OF MIDTERM
5. Solve for x
6. Find the perimeter and area of a rectangle with length 200 ft. and width 15ft
7. A wooden fence is to be built around a 46m y 50m lot. How many meters of fencing will be needed. If the
wood for the fence costs 27.75 per meter, what will the wood for the fence cost
a. 192 m, 5328.00
b. 2300m, 63,825.00
c. 2300m, 5328.00
d. 192m, 63,82500
8. Identify the hyposire and conclusion of the statement/\.
If yesterday was Tuesday, then tomorrow is Thursday
9. “if an obtuse angle is bisected, then two acutes angles are obtained.” Decide whether the statement and its
converse are tru. If false, explain
10. Construct a Venn Diagram for the statement. “I must be a member of the club to use the tennis courts.
11. Given that:
i. No people who make assignments are friendly
ii. All instructors make assignments
What conclusion can be logically deducted?
12. Which of the following is an example of the Symmetric Property?
13. Identify the property of congruence.
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15. Which is a pair of parallel planes?
16. Define Skew Lines
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22. Find the slope of the line passing through the points A(-4,-8) and B(-7,-2)
23. State the relationship between the lines y = -(1/3)x +2 and y= -(1/3)x -2. Explain your answer
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25. Find the slope-intercept form of the line passing through the point (-2, 3) and parallel to line y = 4x – 5
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27. Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither
Line 1 passes through (10, 2) and (5, 6)
Line 2 passes through (4, -6) and (-1, -2)
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29. Complete the state using one of the following words: always, sometimes, or never. “An isosceles triangle is
__________ an obtuse triangle.
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59. Find the coordinates of M if N(1.5, 2.5) is the midpoint of MP and P has coordinates (6, 9)
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61. Find the measurement of each segment. Assume that each figure is not drawn to scale.
62. The pivot or midpoint of a seesaw on a playground is 13.5 from the swing set If the swing is 8 feet from the
edge of the seesaw when the seesaw is level, how long is the seesaw.
63. Determine whether the statement below is true or false. If flase, provide a counterexample.
If AB is perpendicular to CD, then exactly two right angles are formed
64. Use the following statements to write a compound statement for each conjection or disjunction. This find
its truth value. Explain your reasoning.
P: a prism has two bases
Q: A pyramid has two bases
R: A Sphere has no bases
65. Determine whether AB and CD are parallel, perpendicular, or neither. Graph each line to verify your
answer
66. Find the distance between each pair of parallel lines with the given equations.
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68. Classify each triangle as acute, equiangular, obtuse, or right and as equilateral, isosceles, or scalene.
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70. List the angles and sides of each triangle in order from smallest to largest
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72. Find the indicated point of concurrency for each triangle with the given vertices
73. Three cities lie in a triangle as shown. Which two cities are the farthest apart?
74. Write an indirect proof of each statement.
75. Write an indirect proof of the statement below: A triangle can have at most one obtuse angle