Download M2 - Southwest Washington Math

Integrated 2
Mini-EOC 2
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Multiple Choice
M2.3.C Write the converse, inverse, and contrapositive of a valid proposition and
determine their validity.
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1. What is the contrapositive of the statement below?
If a triangle is isosceles, then it has two congruent sides.
 A.
 B.
 C.
 D.
If a triangle does not have two congruent sides, then it is not isosceles.
If a triangle has two congruent sides, then it is isosceles.
If a triangle is isosceles, then it has two congruent sides.
A triangle has two congruent sides if and only if it is isosceles.
Answer: A
http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor
mWS2.pdf
M2.3.E Know, explain, and apply basic postulates and theorems about triangles and
the special lines, line segments, and rays associated with a triangle.
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2. Which of the following statements about this picture is true?
 A.
 B.
 C.
 D.
mO  mM
mM  mN
mM  mN
mN  mO
Answer: B
http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor
mWS2.pdf
Integrated 2
Mini-EOC 2
Answers and Sources
M2.3.G Know, prove, and apply the Pythagorean Theorem and its converse.
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3. Which set of numbers could be the lengths of the sides of a right triangle?
 A.
 B.
 C.
 D.
{10, 24, 26}
{12, 16, 30}
{3, 4, 6}
{4, 7, 8}
Answer: A http://www.jmap.org/JMAP/RegentsExamsandQuestions/2-WordDOCs/WorksheetsByPITopic/Geometry/Informal_and_Formal_Proofs/G.G.48.PythagoreanTheorem.doc
M2.3.H Solve problems involving the basic trigonometric ratios of sine, cosine, and
tangent.
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4. A large totem pole near Kalama, Washington, is 115 ft tall. On a particular day at
noon it casts a 231 ft shadow. What is the sun's angle of elevation at that time?
 A. 29.9°
 B. 63.5°
 C. 60.1°
 D. 26.5°
Answer: Dhttp://www.jmap.org/JMAP/RegentsExamsandQuestions/3AdobePDFs/WorksheetsByPI/Integrated_Algebra/Algebra/Drills/PR_A.A.43.pdf
M2.3.I Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve
problems.
5. Find the length of AD
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Integrated 2
Mini-EOC 2
Answers and Sources
 A. 6 2
 B. 9
 C. 6 3
 D. 12
Answer: A http://www.doe.mass.edu/mcas/2010/release/g10math.pdf
M2.3.J Know, prove, and apply basic theorems about parallelograms.
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6. In parallelogram PQRS the measurers of angle P and angle R are each 146°.
What is the measure of angle Q?
 A. 146°
 B. 112°
 C. 68°
 D. 34°
ANSWER D
M2.3.M Verify and apply properties of triangles and quadrilaterals in the coordinate plane.
7.




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Determine the most precise name for the figure: A(–6, –3), B(1, 0), C(4, 7), D(–3, 4).
A. kite
B. rectangle
C. square
D. rhombus
ANSWER D http://www.jmap.org/JMAP/RegentsExamsandQuestions/3AdobePDFs/WorksheetsByPI/Geometry/Coordinate_Geometry/Drills/PR_G.G.69_2.pdf
M2.6.E Read and interpret diagrams, graphs, and text containing the symbols,
language, and conventions of mathematics.
M2.3.L Determine the coordinates of a point that is described geometrically.
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Integrated 2
Mini-EOC 2
Answers and Sources
8. The county planning department designs a new park in the shape of a parallelogram.
They put in two diagonal walkways.
What will be the coordinates of the intersection of the diagonal walkways?
 A. (6, 2.5)
 B. (5, 6.5)
 C. (5.5, 6)
 D. (6, 5.5)
Answer: D
http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor
mWS2.pdf
Completion Items
M2.3.J Know, prove, and apply basic theorems about parallelograms.
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9. Identify the best name for the quadrilateral formed by the intersection of the lines
listed.
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y  x , y   x  6 , y  x  6 , y   x 18
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Write your answer on the line.
The best name for the quadrilateral is __________________________ .
ANSWER parallelogram [email protected]
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Integrated 2
Mini-EOC 2
Answers and Sources
M2.3.K Know, prove, and apply theorems about properties of quadrilaterals and other
polygons.
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10. Complete the blank statement and reason in the
flowchart proof.
Given: PROE is a rhombus, SPE  VOE
Prove: SE  EV
PROE is a rhombus
Given
SPE  VOE
Given
SPE  VOE
SEP  VEO
ASA
Vertical Angles are
congruent.
Answer:
SE  EV
CPCTC
Writes “PE = OE” or equivalent
Writes “A rhombus has 4 congruent sides” or equivalent
M2.3.L Determine the coordinates of a point that is described geometrically.
11. Points X, Y and Z are collinear. Y is the midpoint of XZ .
The coordinates of point X are (-4, 5). The coordinates of point Z are (8, -3).
Determine the coordinates of point Y.
Write your answer on the line.
What are the coordinates of point Y? ( ____ , ____ )
Answer: (2, 1)
Short Answer
M2.6.B Select and apply strategies to solve problems.
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Integrated 2
Mini-EOC 2
Answers and Sources
M2.5.B Use different degrees of precision in measurement, explain the reason for using a
certain degree of precision, and apply estimation strategies to obtain reasonable
measurements with appropriate precision for a given purpose.
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12. An overhead view of a revolving door is shown in the
accompanying diagram. Each panel is 1.5 meters wide.
What is the approximate width of d, the opening from B to C?
What is the approximate width of d, the opening from B to C? ( ____ , ____ )
Answer: 2.12 m http://www.jmap.org/JMAP/RegentsExamsandQuestions/2WordDOCs/WorksheetsByPITopic/Geometry/Informal_and_Formal_Proofs/G.G.48.PythagoreanTheorem.doc
2-point response: The student shows understanding of selecting and applying
strategies to solve problems by doing the following:
 Writes 2.12 m
 Shows a method that leads to the solution.
1-point response: The student does one of the following:
 Writes 2.12 m
M2.3.F Determine and prove triangle congruence and other properties of triangles.
13. In the diagram AB ≅ EB and
ADB ≅ ECB
Prove ΔABD ≅ ΔEBC using mathematical
language and concepts.
Proof:
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Integrated 2
Mini-EOC 2
Answers and Sources
2-point response: The student shows understanding of proving triangle congruence by
doing the following:
 Writes AB ≅ EB and ∠ADB ≅ ∠ECB (given)
 Writes ∠ABD ≅ ∠CBE by vertical angles, or equivalent
 Writes ΔABD ≅ ΔEBC by Angle-Angle-Side, or equivalent
1-point response: The student does one of the following:
 Writes ∠ABD ≅ ∠CBE by vertical angles, or equivalent
 Writes ΔABD ≅ ΔEBC by Angle-Angle-Side, or equivalent
Note: Student responses may be in the form of a flow chart proof, two-column proof, or
paragraph proof.
Student responses should refer to the given information.
Sample Answers:
Proof: AB ≅ CD Given
∠ADB ≅ ∠ECB Given
∠ABD ≅ ∠CBE Vertical Angles
ΔABD ≅ ΔEBC AAS Congruence
Proof: AB ≅ CD and ∠ADB ≅ ∠ECB are given. ∠ABD ≅ ∠CBE and ∠ABD ≅ ∠CBE are
congruent because vertical angles are congruent. Therefore, ΔABD ≅ ΔEBC by AngleAngle- Side Congruence.

Shows a method that could lead to the solution.