Geometry Final 2012 Review
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____1.The length of is shown. What other length can you determine for this diagram?
a. / EF = 12 / c. / DF = 24b. / DG = 12 / d. / No other length can be determined.
____2.Which statement can you conclude is true from the given information?
Given: is the perpendicular bisector of
a. / AJ = BJ / c. / IJ = JKb. / is a right angle. / d. / A is the midpoint of .
____3.Which statement is not necessarily true?
Given: is the bisector of
a. / DK = KE / c. / K is the midpoint of .b. / / d. / DJ = DL
____4.Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. / I only / b. / II only / c. / I or II only / d. / I, II, or II____5.Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. / I only / b. / III only / c. / I or III only / d. / I, II, or II____6.Where can the medians of a triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. / I only / b. / III only / c. / I or III only / d. / I, II, or II____7.Where can the lines containing the altitudes of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. / I only / b. / I or II only / c. / III only / d. / I, II, or II____8.Which diagram shows a point P an equal distance from points A, B, and C?
a. / / c. /b. / / d. /
____9.Name the smallest angle of The diagram is not to scale.
a. /b. /
c. / Two angles are the same size and smaller than the third.
d. /
____10.Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 ft from camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft apart. Which camera had to cover the greatest angle?
a. / camera 2 / b. / camera 1 / c. / cannot tell / d. / camera 3____11.Jay, Kay, and Ray found themselves far apart when they stopped for lunch while working in a field. Jay could see Kay, then turn through 75° and see Ray. Kay could see Ray, then turn through 50° and see Jay. Ray could see Jay, then turn through 55° and see Kay. Which two were farthest apart?
a. / Kay and Rayb. / Jay and Kay
c. / Ray and Jay
d. / Kay and Ray were the same distance apart as Ray and Jay.
____12.Which three lengths could be the lengths of the sides of a triangle?
a. / 12 cm, 5 cm, 17 cm / c. / 9 cm, 22 cm, 11 cmb. / 10 cm, 15 cm, 24 cm / d. / 21 cm, 7 cm, 6 cm
____13.Which three lengths can NOT be the lengths of the sides of a triangle?
a. / 23 m, 17 m, 14 m / c. / 5 m, 7 m, 8 mb. / 11 m, 11 m, 12 m / d. / 21 m, 6 m, 10 m
____14.Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side?
a. / / c. / x > 10 and x < 18b. / x > 8 and x < 28 / d. /
____15.Two sides of a triangle have lengths 6 and 17. Which expression describes the length of the third side?
a. / at least 11 and less than 23 / c. / greater than 11 and at most 23b. / at least 11 and at most 23 / d. / greater than 11 and less than 23
____16.Judging by appearance, classify the figure in as many ways as possible.
a. / rectangle, square, quadrilateral, parallelogram, rhombusb. / rectangle, square, parallelogram
c. / rhombus, trapezoid, quadrilateral, square
d. / square, rectangle, quadrilateral
____17.Which statement is true?
a. / All quadrilaterals are rectangles.b. / All quadrilaterals are squares.
c. / All rectangles are quadrilaterals.
d. / All quadrilaterals are parallelograms.
____18.Judging by appearances, which figure is a trapezoid?
a. / / c. /b. / / d. /
____19.WXYZ is a parallelogram. Name an angle congruent to
a. / / b. / / c. / / d. /____20.What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
Prove:
Statements / Reasons1. / 1. Definition of parallelogram
2. / 2. Alternate Interior Angles Theorem
3. / 3. Definition of parallelogram
4. / 4. Alternate Interior Angles Theorem
5. / 5. Reflexive Property of Congruence
6. / 6. ?
a. / Reflexive Property of Congruence / c. / Alternate Interior Angles Theorem
b. / ASA / d. / SSS
____21.Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?
a. / / c. /b. / / d. /
____22.Lucinda wants to build a square sandbox, but has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length.
a. / Arrange four equal-length sides so the diagonals bisect each other.b. / Arrange four equal-length sides so the diagonals are equal lengths also.
c. / Make each diagonal the same length as four equal-length sides.
d. / Not possible; Lucinda has to be able to measure a right angle.
____23.Which description does NOT guarantee that a quadrilateral is a parallelogram?
a. / a quadrilateral with both pairs of opposite sides congruentb. / a quadrilateral with the diagonals bisecting each other
c. / a quadrilateral with consecutive angles supplementary
d. / quadrilateral with two opposite sides parallel
____24.Which diagram shows the most useful positioning of a square in the first quadrant of a coordinate plane?
a. / / c. /b. / / d. /
____25.Which diagram shows the most useful positioning and accurate labeling of a kite in the coordinate plane?
a. / / c. /b. / / d. /
Short Answer
26.Identify parallel segments in the diagram.
27.B is the midpoint of and D is the midpoint of Solve for x,given and
28.Given: is the perpendicular bisector of IK. Name two lengths that are equal.
29.In draw median FJ from F to the side opposite F.
30.Write the inverse of this statement:
If a number is divisible by two, then it is even.
31.To prove “p is equal to q” using an indirect proof, what would your starting assumption be?
32.Given points A(2, 3) and B(–2, 5),explain how you could use the Distance Formula and an indirect argument to show that point C(0, 3) is NOT the midpoint of .
33.Can these three segments form the sides of a triangle? Explain.
34.Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
35.What type of quadrilateral has exactly one pair of parallel sides?
36.Isosceles trapezoid ABCD has legs and and base If AB=4y–3, BC =3y–4, and CD=5y – 10, find the value of y.
37.One side of a kite is 6 cm less than 4 times the length of another. The perimeter of the kite is 68 cm. Find the length of each side of the kite.
38.For parallelogram PQRS, find the values of x and y. Then find PT, TR, ST, and TQ. The diagram is not to scale.
39.Complete this statement: For parallelogram ABCD,
Then state a definition or theorem that justifies your answer.
40.Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.
41.Draw two noncongruent kites A and B such that the sides of kite A are congruent to the sides of kiteB.
42.Judging by appearance, classify the figure in as many ways as possible using rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus.
Draw a net for the figure shown. Label the net with its dimensions.
43.
44.
Consider the prism shown below.
a. / Draw a net for the prism and label all dimensions.b. / Use the net to find the surface area of the prism.
45.
46.
Essay
47.Write a two column proof.
Given:
Prove:
48.AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.
49.Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle.
50.A 16-foot ladder is placed against the side of a building as shown in Figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, the ladder is moved 4 feet closer to the base of the building as shown in Figure 2.
To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer.
51.The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim? Show your work.
52.Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter.
53.Erica made a cylindrical pottery vase with a height of 45 cm and a diameter of 14 cm.
a. / Erica wants to paint just the sides of the vase. To the nearest whole number, find the number of square centimeters she will need to paint. Explain the method you use to find the lateral area.b. / Erica’s friend Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you use to find the radius.
54.A log cabin is shaped like a rectangular prism. A model of the cabin has a scale of 1 centimeter to 0.5 meters.
a. / If the model is 14 cm by 20 cm by 7 cm, what are the dimensions of the actual log cabin? Explain how you find the dimensions.b. / What is the volume of the actual log cabin? Explain how you find the volume.
c. / What is the ratio of the volume of the model of the cabin to the volume of the actual cabin? Explain your method for finding the ratio.
55.A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.
Other
56.A conditional statement and its contrapositive have the same truth value and are called equivalent statements. How are the inverse and converse of a conditional statement related to each other?
57.A tennis court has a baseline at each end. One is labeled in the picture. Which part of the tennis court is equidistant from the midpoints of the two baselines? Explain.
58.ABCD is a rhombus. Explain why .
59.Is the quadrilateral a parallelogram? Explain. The diagram is not to scale.
60.All of the angles of a quadrilateral are congruent. Can the quadrilateral be a parallelogram? Explain.
61.Can this quadrilateral be a parallelogram? Explain.
62.A triangle has sides that measure 33 cm, 65 cm, and 56 cm. Is it a right triangle? Explain.
63.Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
a. / What is the volume of the cylinder? Explain your method for finding the volume.b. / What is the total volume of the three balls? Explain your method for finding the total volume.
c. / What percent of the volume of the container is occupied by the three balls? Explain how you find the percent.
64.Katie approximated the volume and the surface area for a ball she was using for some exercises by assuming the ball is a sphere. She was surprised when the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. What is the radius of the ball? Explain your method for finding the radius.
Geometry Final 2012 Review
Answer Section
MULTIPLE CHOICE
1.ANS:ADIF:L1REF:5-2 Bisectors in Triangles
OBJ:5-2.1 Perpendicular Bisectors and Angle BisectorsSTO:NJ 4.2.A.3
TOP:5-2 Example 1KEY:perpendicular bisector,Perpendicular Bisector Theorem
MSC:NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16
2.ANS:CDIF:L2REF:5-2 Bisectors in Triangles
OBJ:5-2.1 Perpendicular Bisectors and Angle BisectorsSTO:NJ 4.2.A.3
KEY:perpendicular bisector,Perpendicular Bisector Theorem,reasoning
MSC:NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16
3.ANS:ADIF:L2REF:5-2 Bisectors in Triangles
OBJ:5-2.1 Perpendicular Bisectors and Angle BisectorsSTO:NJ 4.2.A.3
KEY:Perpendicular Bisector Theorem,perpendicular bisector,reasoning
MSC:NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16
4.ANS:BDIF:L3REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.1 Properties of BisectorsSTO:NJ 4.2.A.3
KEY:circumcenter of the triangle,perpendicular bisector,reasoning,right triangle
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
5.ANS:ADIF:L2REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.1 Properties of BisectorsSTO:NJ 4.2.A.3
KEY:incenter of the triangle,angle bisector,reasoning
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
6.ANS:ADIF:L2REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.2 Medians and AltitudesSTO:NJ 4.2.A.3
KEY:median of a triangle,centroid,reasoning
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
7.ANS:CDIF:L2REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.2 Medians and AltitudesSTO:NJ 4.2.A.3
KEY:altitude of a triangle,orthocenter of the triangle
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
8.ANS:ADIF:L1REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.1 Properties of BisectorsSTO:NJ 4.2.A.3TOP:5-3 Example 2
KEY:circumcenter of the triangle,circumscribe
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
9.ANS:DDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.1 Inequalities Involving Angles of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 2KEY:Theorem 5-10
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
10.ANS:DDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.1 Inequalities Involving Angles of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 2KEY:word problem,problem solving,Theorem 5-10
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
11.ANS:ADIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 3KEY:problem solving,word problem,Theorem 5-11
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
12.ANS:BDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 4KEY:Triangle Inequality Theorem
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
13.ANS:DDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 4KEY:Triangle Inequality Theorem
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
14.ANS:BDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 5KEY:Triangle Inequality Theorem
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
15.ANS:DDIF:L1REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
TOP:5-5 Example 5KEY:Triangle Inequality Theorem
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
16.ANS:ADIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
TOP:6-1 Example 1
KEY:special quadrilaterals,quadrilateral,parallelogram,rhombus,square,rectangle,kite,trapezoid
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
17.ANS:CDIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
KEY:reasoning,kite,parallelogram,quadrilateral,rectangle,rhombus,special quadrilaterals
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
18.ANS:BDIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
KEY:trapezoid
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
19.ANS:DDIF:L1REF:6-2 Properties of Parallelograms
OBJ:6-2.1 Properties: Sides and AnglesSTO:NJ 4.2.A.3KEY:parallelogram,opposite angles
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16
20.ANS:BDIF:L2REF:6-2 Properties of Parallelograms
OBJ:6-2.2 Properties: Diagonals and TransversalsSTO:NJ 4.2.A.3
KEY:proof,two-column proof,parallelogram,diagonal
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16
21.ANS:ADIF:L2REF:6-3 Proving That a Quadrilateral is a Parallelogram
OBJ:6-3.1 Is the Quadrilateral a Parallelogram?STO:NJ 4.2.A.3
KEY:proof,reasoning,parallelogram
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16, TV.LV20.17, TV.LV20.18
22.ANS:BDIF:L2REF:6-4 Special Parallelograms
OBJ:6-4.2 Is the Parallelogram a Rhombus or a Rectangle?STO:NJ 4.2.A.3
TOP:6-4 Example 4
KEY:square,reasoning,Theorem 6-10,Theorem 6-11,word problem,problem solving
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
23.ANS:DDIF:L2REF:6-4 Special Parallelograms
OBJ:6-4.2 Is the Parallelogram a Rhombus or a Rectangle?STO:NJ 4.2.A.3
KEY:square,reasoning
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
24.ANS:CDIF:L1REF:6-6 Placing Figures in the Coordinate Plane
OBJ:6-6.1 Naming CoordinatesSTO:NJ 4.2.C.1
KEY:algebra,coordinate plane,rectangle,square
MSC:NAEP G4d, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.17, TV.LV20.52
25.ANS:DDIF:L2REF:6-6 Placing Figures in the Coordinate Plane
OBJ:6-6.1 Naming CoordinatesSTO:NJ 4.2.C.1
KEY:algebra,coordinate plane,isosceles trapezoid,kite
MSC:NAEP G4d, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.17, TV.LV20.52
SHORT ANSWER
26.ANS:
DIF:L1REF:5-1 Midsegments of Triangles
OBJ:5-1.1 Using Properties of MidsegmentsSTO:NJ 4.2.A.3
TOP:5-1 Example 2KEY:midsegment,parallel lines,Triangle Midsegment Theorem
MSC:NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
27.ANS:
DIF:L2REF:5-1 Midsegments of Triangles
OBJ:5-1.1 Using Properties of MidsegmentsSTO:NJ 4.2.A.3
KEY:Triangle Midsegment Theorem,midsegment
MSC:NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
28.ANS:
IJ and JK
DIF:L1REF:5-2 Bisectors in Triangles
OBJ:5-2.1 Perpendicular Bisectors and Angle BisectorsSTO:NJ 4.2.A.3
TOP:5-2 Example 1KEY:perpendicular bisector,Perpendicular Bisector Theorem
MSC:NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16
29.ANS:
DIF:L1REF:5-3 Concurrent Lines¸ Medians¸ and Altitudes
OBJ:5-3.2 Medians and AltitudesSTO:NJ 4.2.A.3KEY:median of a triangle
MSC:NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
30.ANS:
If a number is not divisible by two¸ then it is not even.
DIF:L1REF:5-4 Inverses¸ Contrapositives¸ and Indirect Reasoning
OBJ:5-4.1 Writing the Negation¸ Inverse¸ and ContrapositiveSTO:NJ 4.2.A.4
TOP:5-4 Example 2KEY:contrapositive,conditional statement,inverse
MSC:NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17
31.ANS:
p is not equal to q.
DIF:L1REF:5-4 Inverses¸ Contrapositives¸ and Indirect Reasoning
OBJ:5-4.2 Using Indirect ReasoningSTO:NJ 4.2.A.4TOP:5-4 Example 3
KEY:indirect reasoning,indirect proof
MSC:NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17
32.ANS:
Assume that C(0, 3) is the midpoint of . By the Distance Formula,
AC BCwhich contradicts the assumption that C is the midpoint of .
Therefore, C is not the midpoint of.
DIF:L2REF:5-4 Inverses¸ Contrapositives¸ and Indirect Reasoning
OBJ:5-4.2 Using Indirect ReasoningSTO:NJ 4.2.A.4
KEY:indirect proof,indirect reasoning,Distance Formula,proof
MSC:NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17
33.ANS:
No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater than the length of the third segment.
DIF:L2REF:5-5 Inequalities in Triangles
OBJ:5-5.2 Inequalities Involving Sides of TrianglesSTO:NJ 4.2.A.3
KEY:Triangle Inequality Theorem
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
34.ANS:
x = 7, y = 4; 20, 35
DIF:L2REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
TOP:6-1 Example 3KEY:algebra,rectangle
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
35.ANS:
trapezoid
DIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
KEY:quadrilateral,reasoning,algebra,trapezoid,rhombus,square,parallelogram
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
36.ANS:
7
DIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
KEY:isosceles trapezoid,algebra
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
37.ANS:
8 cm , 26 cm
DIF:L1REF:6-1 Classifying Quadrilaterals
OBJ:6-1.1 Classifying Special QuadrilateralsSTO:NJ 4.2.A.3
KEY:kite,algebra,word problem,problem solving
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
38.ANS:
x = 3, y = 6; 5, 5, 7, 7
DIF:L2REF:6-2 Properties of Parallelograms
OBJ:6-2.2 Properties: Diagonals and TransversalsSTO:NJ 4.2.A.3
TOP:6-2 Example 3KEY:parallelogram,algebra,multi-part question
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16
39.ANS:
OD; the diagonals of a parallelogram bisect each other.
DIF:L1REF:6-2 Properties of Parallelograms
OBJ:6-2.2 Properties: Diagonals and TransversalsSTO:NJ 4.2.A.3
KEY:parallelogram,diagonal,Theorem 6-3
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16
40.ANS:
Rhombus; the measure of all numbered angles equal 39.
DIF:L1REF:6-4 Special Parallelograms
OBJ:6-4.1 Diagonals of Rhombuses and RectanglesSTO:NJ 4.2.A.3
KEY:parallelogram,rhombus,reasoning
MSC:NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16
41.ANS:
Answers may vary. Sample: