Math: Foundations of Geometry

Which mathematical terms are necessary to form a precise definition of line segment? Check all that apply.

point line

Which are undefined terms that can be used to define other terms?

point, line, plane

Which mathematical term is undefined?

A. line

Which mathematical term cannot be precisely defined?

B. point

Which represents two rays that intersect at a common endpoint?

an angle

Analyze the diagram below and complete the instructions that follow. If point N is in the interior of MPO, find NPO if MPN=57 and MPO=64 A. 2004-01-01-03-00_files/i0320005.jpg B. 2004-01-01-03-00_files/i0320006.jpg C. 2004-01-01-03-00_files/i0320007.jpg D. 2004-01-01-03-00_files/i0320008.jpg Please select the best answer from the choices provided

A. 7

Let W be a point between points U and V on UZ. If UV = 13, UW = 2y - 9, and WV = y - 5, solve for y. A. 9 B. 11 C. 13 D. 27 Please select the best answer from the choices provided

A. 9

Analyze the diagram below and answer the question that follows. Which of the following is not a name for the line above? A. 2004-01-01-02-00_files/i0020001.jpg B. 2004-01-01-02-00_files/i0020002.jpg C. 2004-01-01-02-00_files/i0020003.jpg D. 2004-01-01-02-00_files/i0020004.jpg Please select the best answer from the choices provided

A. BA

Analyze the number line below and answer the question that follows. If FG=HI, where could point I be? A. -7 B. -6 C. -5 D. -4 Please select the best answer from the choices provided

A. -7

Analyze the diagram below and answer the questions that follow. / How many different ways can this ray be named? What are those names? A. 1 way; 2004-01-01-02-00_files/i0330001.jpg B. 1 way; 2004-01-01-02-00_files/i0330004.jpg C. 2 ways; 2004-01-01-02-00_files/i0330002.jpg, 2004-01-01-02-00_files/i0330003.jpg D. 2 ways; 2004-01-01-02-00_files/i0330005.jpg, 2004-01-01-02-00_files/i0330006.jpg Please select the best answer from the choices provided

A. 1 way; RQ

Analyze the diagram below and answer the question that follows. If OLN=31 and MLO=52, what is MLN? A. 2004-01-01-03-00_files/i0210004.jpg B. 2004-01-01-03-00_files/i0210005.jpg C. 2004-01-01-03-00_files/i0210006.jpg D. 2004-01-01-03-00_files/i0210007.jpg Please select the best answer from the choices provided

A. 21

Analyze the diagram below and complete the instructions that follow. 2004-01-01-03-00_files/i0310004.jpg If N is in the interior of MPO, find NPO if MPN=57 and MPO=81. A. 2004-01-01-03-00_files/i0310005.jpg B. 2004-01-01-03-00_files/i0310006.jpg C. 2004-01-01-03-00_files/i0310007.jpg D. 2004-01-01-03-00_files/i0310008.jpg Please select the best answer from the choices provided

A. 24

Analyze the image below and complete the instructions that follow. 2004-01-01-03-00_files/i0080000.jpg Image by Jane M. Sawyer Estimate the measure of the clockwise angle formed by the minute hand and the second hand, then classify the angle. A. 54°; acute B. 75°; acute C. 86°; right D. 145°; obtuse Please select the best answer from the choices provided

A. 54; acute

If M is the midpoint of LN and LN=27.8, find the length of MN A. 13.8 B. 13.9 C. 14.2 D. 14.5 Please select the best answer from the choices provided

B. 13.9

Analyze the diagram below and answer the question that follows. Which statement about the intersecting line and segment is false? A. 2004-01-01-04-00_files/i0040001.jpg is a perpendicular bisector of 2004-01-01-04-00_files/i0040002.jpg. B. 2004-01-01-04-00_files/i0040003.jpg is a bisector of 2004-01-01-04-00_files/i0040004.jpg. C. 2004-01-01-04-00_files/i0040005.jpg D. 2004-01-01-04-00_files/i0040006.jpg Please select the best answer from the choices provided

A. DB is a perpendicular bisector of AC.

Analyze the diagram below and answer the question that follows. YA bisects XYZ. Which statement is false? A. / B. 2004-01-01-04-00_files/i0320004.jpg and 2004-01-01-04-00_files/i0320005.jpg each measure 2004-01-01-04-00_files/i0320006.jpg. C. 2004-01-01-04-00_files/i0320007.jpg D. The total measure of 2004-01-01-04-00_files/i0320008.jpg and 2004-01-01-04-00_files/i0320009.jpg is 2004-01-01-04-00_files/i0320010.jpg. Please select the best answer from the choices provided

A. YX=YZ

Mile markers along the highway tell drivers how many miles they have traveled from one location to another. Suppose Daniel sees mile marker 141 when he gets onto the highway and mile marker 67 when he exits the highway. How far did Daniel travel on the highway? A. 69 miles B. 71 miles C. 74 miles D. 208 miles Please select the best answer from the choices provided

C.

If B is the midpoint of AC and the length of AC is 23.8, what is the length of AB? A. 11.7 B. 11.9 C. 12.4 D. 19.1 Please select the best answer from the choices provided

B. 11.9

Analyze the diagram below and complete the instructions that follow. If D is the midpoint of EG, find the length of EG A. 6 B. 12 C. 18 D. 21 Please select the best answer from the choices provided

B. 12

Which mathematical term can be defined precisely?

D. circle

Analyze the diagram below and answer the question that follows. 2004-01-01-03-00_files/i0110000.jpg Assuming that line WXZ is straight, what are the measure and the classification of angle YXZ? A. 2004-01-01-03-00_files/i0110001.jpg; obtuse B. 2004-01-01-03-00_files/i0110002.jpg; obtuse C. 2004-01-01-03-00_files/i0110003.jpg; acute D. 2004-01-01-03-00_files/i0110004.jpg; straight Please select the best answer from the choices provided

B. 135; obtuse

Point M is between points N and O on NO. Find the length of NM if MO = 12.3 and NO = 26.9. A. 11.6 B. 14.6 C. 21.6 D. 38.2 Please select the best answer from the choices provided

B. 14.6

Analyze the diagram below and complete the instructions that follow. If GI bisects FGH, find HGI. A. 2004-01-01-04-00_files/i0250004.jpg B. 2004-01-01-04-00_files/i0250005.jpg C. 2004-01-01-04-00_files/i0250006.jpg D. 2004-01-01-04-00_files/i0250007.jpg Please select the best answer from the choices provided

B. 23

Analyze the diagram below and answer the question that follows. If LM is the angle bisector of NLK and NLK=72, what is KLM A. 2004-01-01-04-00_files/i0070005.jpg B. 2004-01-01-04-00_files/i0070006.jpg C. 2004-01-01-04-00_files/i0070007.jpg D. 2004-01-01-04-00_files/i0070008.jpg Please select the best answer from the choices provided

B. 36

The centers of Marathon County, Bayfield County, and Dodge County all lie along a straight road. If Marathon County is equidistant from Bayfield County and Dodge County, what is the distance from Bayfield County to Dodge County if the distance from Marathon County to Dodge County is 487 miles? A. 964 miles B. 974 miles C. 984 miles D. 994 miles Please select the best answer from the choices provided

B. 947 miles

Analyze the diagram below and complete the instructions that follow. Image by Scientif38 Find POT. A. 2004-01-01-03-00_files/i0410002.jpg B. 2004-01-01-03-00_files/i0410003.jpg C. 2004-01-01-03-00_files/i0410004.jpg D. 2004-01-01-03-00_files/i0410005.jpg Please select the best answer from the choices provided

B. 98

If GH is the angle bisector of FGI, which statement about the angle is true? A. 2004-01-01-04-00_files/i0030002.jpg B. 2004-01-01-04-00_files/i0030003.jpg C. Point I is the vertex. D. 2004-01-01-04-00_files/i0030004.jpg Please select the best answer from the choices provided

B. FGH=IGH

Analyze the diagram below and answer the question that follows. MN What is a name of the line segment above? A. 2004-01-01-02-00_files/i0080001.jpg B. 2004-01-01-02-00_files/i0080002.jpg C. 2004-01-01-02-00_files/i0080003.jpg D. 2004-01-01-02-00_files/i0080004.jpg Please select the best answer from the choices provided

B. NM

When a ray bisects an angle, it does all of the following except what? A. divides the angle into two congruent angles B. contains the vertex of the angle C. lies in the interior of the angle D. shares a side with the angle Please select the best answer from the choices provided

D. shares a side with the angle

Analyze the diagram below and complete the instructions that follow. 2004-01-01-04-00_files/i0170000.jpg If NS bisects QNR, find QNR. A. 2004-01-01-04-00_files/i0170004.jpg B. 2004-01-01-04-00_files/i0170005.jpg C. 2004-01-01-04-00_files/i0170006.jpg D. 2004-01-01-04-00_files/i0170007.jpg Please select the best answer from the choices provided

C. 102

Analyze the diagram below and complete the instructions that follow. LN bisects KLM into two congruent angles measuring (3x-4) and (4x-27) Find mKLM. A. 65 B. 75 C. 130 D. 155 Please select the best answer from the choices provided

C. 130

Analyze the diagram below and complete the instructions that follow. / The KLM that is measured at 220° is a reflex angle. The opposite angle is obtuse. Find the measure of obtuse KLM. A. 40° B. 130° C. 140° D. 200° Please select the best answer from the choices provided

C. 140

Find the length of a line segment with endpoints of -9 and 7. A. -16 B. -2 C. 16 D. 26 Please select the best answer from the choices provided

C. 16

Analyze the diagram below and complete the instructions that follow. Photo by Luigi Chiesa Use the ruler postulate to calculate the distance between P, which is at 7, and Q, which is at 24. A. 15 B. 16 C. 17 D. 18 Please select the best answer from the choices provided

C. 17

Let point C be between V and W on VW. Given that VW = 61, VC = z + 13, and CW = z + 8, solve for z. A. 18 B. 19 C. 20 D. 21 Please select the best answer from the choices provided

C. 20

Analyze the diagram below and complete the instructions that follow. If P is the midpoint of QR, find the length of QR A. 37 B. 38 C. 40 D. 43 Please select the best answer from the choices provided

C. 40

Analyze the diagram below and complete the instructions that follow. / Image by Scientif38 Find POS. A. 2004-01-01-03-00_files/i0160002.jpg B. 2004-01-01-03-00_files/i0160003.jpg C. 2004-01-01-03-00_files/i0160004.jpg D. 2004-01-01-03-00_files/i0160005.jpg Please select the best answer from the choices provided

C. 85

Analyze the diagram below and complete the instructions that follow. / Image by Scientif38 Name two congruent angles that measure 15. A. 2004-01-01-03-00_files/i0170002.jpg and 2004-01-01-03-00_files/i0170003.jpg B. 2004-01-01-03-00_files/i0170004.jpg and 2004-01-01-03-00_files/i0170005.jpg C. 2004-01-01-03-00_files/i0170006.jpg and 2004-01-01-03-00_files/i0170007.jpg D. 2004-01-01-03-00_files/i0170008.jpg and 2004-01-01-03-00_files/i0170009.jpg Please select the best answer from the choices provided

C. NOP and ROS

Haley draws a timeline. Point B marks the moment of her birth, and point C measures the current time. Which is true about the distance between the two points?

C. The distance between the two points is undefined unless a unit of time is defined.

WV bisects XYW. The measure of angle XWV is (x+3), and the measure of angle VWY is (3x-91). Solve for x. A. x = 29 B. x = 33 C. x = 47 D. x = 48 Please select the best answer from the choices provided

C. x=47

Analyze the diagram below and complete the instructions that follow. If point H is in the interior of GJI, find GJI A. 2004-01-01-03-00_files/i0300003.jpg B. 2004-01-01-03-00_files/i0300004.jpg C. 2004-01-01-03-00_files/i0300005.jpg D. 2004-01-01-03-00_files/i0300006.jpg Please select the best answer from the choices provided

D. 139

If W is the midpoint of VX and WX=7.8, find the length of VX A. 3.9 B. 14.7 C. 15.2 D. 15.6 Please select the best answer from the choices provided

D. 15.6

Point D is between points R and S on RS. Find the length of RS if RD = 7 and DS = 12. A. 1 B. 5 C. 18 D. 19 Please select the best answer from the choices provided

D. 19

Analyze the diagram below and answer the question that follows. If IJ = 15 and JK = 8, what is IK? A. 5 B. 7 C. 22 D. 23 Please select the best answer from the choices provided

D. 23

Analyze the diagram below and answer the questions that follow. / How many names does the angle have? What are those names? A. 3 names: 2004-01-01-03-00_files/i0100001.jpg, 2004-01-01-03-00_files/i0100002.jpg, 2004-01-01-03-00_files/i0100003.jpg B. 3 names: 2004-01-01-03-00_files/i0100008.jpg, 2004-01-01-03-00_files/i0100009.jpg, 2004-01-01-03-00_files/i0100010.jpg C. 4 names: 2004-01-01-03-00_files/i0100004.jpg, 2004-01-01-03-00_files/i0100005.jpg, 2004-01-01-03-00_files/i0100006.jpg, 2004-01-01-03-00_files/i0100007.jpg D. 4 names: 2004-01-01-03-00_files/i0100011.jpg, 2004-01-01-03-00_files/i0100012.jpg, 2004-01-01-03-00_files/i0100013.jpg, 2004-01-01-03-00_files/i0100014.jpg Please select the best answer from the choices provided

D. 4 names: 3, T, STU, UTS

ABD and CBD are adjacent. Given that ABC is 68, ABD=(2x+5), and CBD=(3x+8), find CBD. A. 2004-01-01-03-00_files/i0220005.jpg B. 2004-01-01-03-00_files/i0220006.jpg C. 2004-01-01-03-00_files/i0220007.jpg D. 2004-01-01-03-00_files/i0220008.jpg Please select the best answer from the choices provided

D. 41

Find the length of a line segment with endpoints of 19 and -39. A. -58 B. -20 C. 20 D. 58 Please select the best answer from the choices provided

D. 58

Analyze the diagram below and answer the question that follows. 2004-01-01-04-00_files/i0150000.jpg YC bisects AYB. What is AYB if BYC=33? A. 2004-01-01-04-00_files/i0150005.jpg B. 2004-01-01-04-00_files/i0150006.jpg C. 2004-01-01-04-00_files/i0150007.jpg D. 2004-01-01-04-00_files/i0150008.jpg Please select the best answer from the choices provided

D. 66

Analyze the line below and answer the question that follows. What is a name of the line? A. 2004-01-01-02-00_files/i0180001.jpg B. 2004-01-01-02-00_files/i0180002.jpg C. 2004-01-01-02-00_files/i0180003.jpg D. 2004-01-01-02-00_files/i0180004.jpg Please select the best answer from the choices provided

D. JI

Which statement is true about the distance formula, d=(x2-x1)2+(v2-v1)2, when describing the distance along a line segment?

It is not a precise definition because it is based on an understanding of coordinates, which are defined based on the distance of a line segment.

Consider the description of a circle. A circle is the set of all points in a plane that are equidistant from a common point. Which statements are true about the description? Check all that apply.

The description is sufficient to describe all cases of a circle. The description includes only necessary information to describe a circle. The description is a mathematically precise definition of a circle.

Which is a description of an undefined term?

The distance along a line segment is the number of units between two points.

Gray looks up the definition of point. A point is a location in a region. What is true about the statement describing the word point?

The statement uses the terms location and region that are defined based on an understanding of a point.

If you have a protractor that only measures 0 to 90 degrees, explain how to use this protractor to find the measure of an obtuse angle.

You would use the protractor to first find 90 degrees of the angle and then to measure the remaining part of the angle. then add 90 and the second value together. OR Align the protractor with one side of the angle, then make a tick mark at 90 degrees. Next, keeping the center point of the protractor at the vertex of the angle, rotate the protractor so that the 0 degree mark is at the tick mark you drew. Measure the angle between your tick mark and the other side of the angle, then add this measure to 90 degrees to get the measure of the obtuse angle.

Which is an example of a line segment?

the edge of a book