Geometry - Unit 1 Assessment – Tools of Geometry
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1.Based on the pattern, make a conjecture about the sum of the first 20 positive even numbers.
2 / = / 2 / = /2 + 4 / = / 6 / = /
2 + 4 + 6 / = / 12 / = /
2 + 4 + 6 + 8 / = / 20 / = /
2 + 4 + 6 + 8 + 10 / = / 30 / = /
a. / The sum is . / c. / The sum is .
b. / The sum is . / d. / The sum is .
2.Find a counterexample to show that the conjecture is false.
Conjecture: Any number that is divisible by 4 is also divisible by 8.
a. / 24 / b. / 40 / c. / 12 / d. / 263.Are O, N, and P collinear? If so, name the line on which they lie.
a. / No, the three points are not collinear.b. / Yes, they lie on the line MP.
c. / Yes, they lie on the line NP.
d. / Yes, they lie on the line MO.
4.Name the plane represented by the front of the box.
a. / FBC / b. / BAD / c. / FEC / d. / FKG5.What is the intersection of plane TUYX and plane VUYZ?
a. / / b. / / c. / / d. /6.Name a fourth point in plane TUW.
a. / Y / b. / Z / c. / W / d. / X7.Which diagram shows plane PQR and plane QRS intersecting only in ?
a. / / c. /b. / / d. /
8.Name the ray that is opposite
a. / / b. / / c. / / d. /9.Name the four labeled segments that are skew to
a. / , , , / c. / , , ,b. / , , , / d. / , , ,
10.How many pairs of skew lines are shown?
a. / 24 / b. / 12 / c. / 48 / d. / 411.Which plane is parallel to plane EFHG?
a. / plane ABDC / b. / plane ACGE / c. / plane CDHG / d. / plane BDHF12.If find the values of x, EF, and FG. The drawing is not to scale.
a. / x =10, EF = 8, FG = 15 / c. / x =10, EF = 32, FG = 45b. / x =3, EF = –6, FG = –6 / d. / x =3, EF = 8, FG = 15
13.If T is the midpoint of find the values of x and ST. The diagram is not to scale.
a. / x = 5, ST = 45 / c. / x = 10, ST = 60b. / x = 5, ST = 60 / d. / x = 10, ST = 45
14.Which point is the midpoint of ?
a. / D / b. / B / c. / not B, C, or D / d. / C15.If and , then what is the measure of The diagram is not to scale.
a. / 64 / b. / 12 / c. / 52 / d. / 7616. bisects , , . Find . The diagram is not to scale.
a. / 61 / b. / 45.75 / c. / 91.5 / d. / 66Student Produce Response
17.Name line p in three other ways.
18.Name four rays shown.
19.On a number line, P has coordinate –47 and Q has coordinate 40. Find PQ.
20.What are three names for the angle?
21.You live in Salt Lake City, Utah, which has approximate (latitude, longitude) coordinates of (41N,112W). Your friend lives in Goodwin, Arkansas, with coordinates of (35N,91W). You plan to meet halfway between the two cities. Find the coordinates of the halfway point.
22.Describe a real-life example of two planes and their intersection.
Free Response
23.Find the measures of PMN and NMR if bisects PMR. The measure of PMR is 136 Draw a sketch that shows the given information. Explain your answer.
24.If is opposite and is opposite , what can you conclude? Explain.
Geometry - Chapter 1 Test
Answer Section
MULTIPLE CHOICE
1.ANS:ADIF:L1REF:1-1 Patterns and Inductive Reasoning
OBJ:1-1.1 Using Inductive ReasoningSTO:MD 1.1.1, MD 1.1.2
TOP:1-1 Example 2KEY:inductive reasoning,pattern,conjecture
MSC:NAEP G5a, CAT5.LV20.47, CAT5.LV20.54, IT.LV16.CP, IT.LV16.I, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17, TV.LV20.49
2.ANS:CDIF:L1REF:1-1 Patterns and Inductive Reasoning
OBJ:1-1.1 Using Inductive ReasoningSTO:MD 1.1.1, MD 1.1.2
TOP:1-1 Example 3KEY:conjecture,counterexample
MSC:NAEP G5a, CAT5.LV20.47, CAT5.LV20.54, IT.LV16.CP, IT.LV16.I, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17, TV.LV20.49
3.ANS:ADIF:L1REF:1-2 Points¸ Lines¸ and Planes
OBJ:1-2.1 Basic Terms of GeometrySTO:MD 2.1.1, MD 2.2.3
TOP:1-2 Example 1KEY:point,line,collinear points
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
4.ANS:ADIF:L1REF:1-2 Points¸ Lines¸ and Planes
OBJ:1-2.1 Basic Terms of GeometrySTO:MD 2.1.1, MD 2.2.3
TOP:1-2 Example 2KEY:plane
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
5.ANS:ADIF:L1REF:1-2 Points¸ Lines¸ and Planes
OBJ:1-2.2 Basic Postulates of GeometrySTO:MD 2.1.1, MD 2.2.3
TOP:1-2 Example 3KEY:plane,intersection of two planes
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
6.ANS:BDIF:L2REF:1-2 Points¸ Lines¸ and Planes
OBJ:1-2.2 Basic Postulates of GeometrySTO:MD 2.1.1, MD 2.2.3
TOP:1-2 Example 4KEY:point,plane
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
7.ANS:CDIF:L1REF:1-2 Points¸ Lines¸ and Planes
OBJ:1-2.2 Basic Postulates of GeometrySTO:MD 2.1.1, MD 2.2.3
TOP:1-2 Example 3KEY:plane,intersection of two planes
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
8.ANS:ADIF:L1REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.1 Identifying Segments and RaysSTO:MD 2.1.1
TOP:1-3 Example 1KEY:ray,opposite rays
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
9.ANS:ADIF:L1REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.2 Recognizing Parallel FiguresSTO:MD 2.1.1TOP:1-3 Example 2
KEY:segment,skew lines
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
10.ANS:ADIF:L3REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.2 Recognizing Parallel FiguresSTO:MD 2.1.1TOP:1-3 Example 2
KEY:parallel lines,skew lines,intersecting lines,collinear points
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
11.ANS:ADIF:L1REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.2 Recognizing Parallel FiguresSTO:MD 2.1.1TOP:1-3 Example 3
KEY:parallel planes
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
12.ANS:ADIF:L1REF:1-4 Measuring Segments and Angles
OBJ:1-4.1 Finding Segment LengthsSTO:MD 2.1.1TOP:1-4 Example 2
KEY:segment,segment length
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
13.ANS:ADIF:L1REF:1-4 Measuring Segments and Angles
OBJ:1-4.1 Finding Segment LengthsSTO:MD 2.1.1TOP:1-4 Example 3
KEY:segment,segment length,midpoint,multi-part question
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
14.ANS:ADIF:L2REF:1-4 Measuring Segments and Angles
OBJ:1-4.1 Finding Segment LengthsSTO:MD 2.1.1TOP:1-4 Example 3
KEY:segment length,segment,midpoint
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
15.ANS:ADIF:L1REF:1-4 Measuring Segments and Angles
OBJ:1-4.2 Finding Angle MeasuresSTO:MD 2.1.1TOP:1-4 Example 6
KEY:Angle Addition Postulate
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
16.ANS:ADIF:L2REF:1-5 Basic Constructions
OBJ:1-5.2 Constructing BisectorsSTO:MD 2.1.4TOP:1-5 Example 4
KEY:angle bisector
MSC:NAEP G3b, 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
Student Produce Response
17.ANS:
Answers may vary. Sample:
DIF:L1REF:1-2 Points¸ Lines¸ and PlanesOBJ:1-2.1 Basic Terms of Geometry
STO:MD 2.1.1, MD 2.2.3TOP:1-2 Example 1
KEY:point,line
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
18.ANS:
Answers may vary. Sample:
DIF:L1REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.1 Identifying Segments and RaysSTO:MD 2.1.1
TOP:1-3 Example 1KEY:point,ray
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
19.ANS:
87
DIF:L1REF:1-4 Measuring Segments and Angles
OBJ:1-4.1 Finding Segment LengthsSTO:MD 2.1.1KEY:segment,segment length
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
20.ANS:
Answers may vary. Sample:
DIF:L1REF:1-4 Measuring Segments and Angles
OBJ:1-4.2 Finding Angle MeasuresSTO:MD 2.1.1TOP:1-4 Example 4
KEY:angle
MSC:NAEP M1e, NAEP M1f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
21.ANS:
(38N, 101.5W)
DIF:L2REF:1-6 The Coordinate PlaneOBJ:1-6.2 Finding the Midpoint of a Segment
STO:MD 2.1.2KEY:Midpoint Formula,coordinate plane
MSC:NAEP M1e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
22.ANS:
Answers may vary. Sample: two walls of a room intersecting to form a vertical corner line.
DIF:L2REF:1-2 Points¸ Lines¸ and PlanesOBJ:1-2.2 Basic Postulates of Geometry
STO:MD 2.1.1, MD 2.2.3KEY:intersection of two planes,plane
MSC:NAEP G1c, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14
Free Response
23.ANS:
[4] /mPMN = mNMR = 68. Since bisects PMR, mPMN = mNMR. By the Angle Addition Postulate, mPMN + mNMR = mPMR. By Substitution, mPMN + mPMN = mPMR, or 2mPMN = mPMR. Thus, mPMN = mPMR = (136) = 68, and mNMR = 68 as well.
[3] / finds correct angle measures and gives explanation, but no diagram
[2] / finds correct angle measures and draws correct diagram, but incomplete or incorrect explanation
[1] / finds correct angle measures only
DIF:L2REF:1-5 Basic ConstructionsOBJ:1-5.2 Constructing Bisectors
STO:MD 2.1.4KEY:angle bisector,Angle Addition Postulate,extended response,rubric-based question
MSC:NAEP G3b, 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:
= . Sample explanation: Both rays have endpoint A and extend in the direction away from point C.
DIF:L2REF:1-3 Segments¸ Rays¸ Parallel Lines and Planes
OBJ:1-3.1 Identifying Segments and RaysSTO:MD 2.1.1
KEY:opposite rays,ray,reasoning
MSC:NAEP G3g, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14