Match between columns Premises: Every two spheres are similar. A chord is a diameter. If Earth were a perfect sphere, then the equator would be considered a minor circle. A diameter is a chord.

The Answer of False and True is...

Exam 21: Curves, Constructions, and Curved Surfaces

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Draw a line m and a point P not on the line. With a compass and a straightedge, construct a line through point P that is parallel to line m. Do not erase any key construction marks.

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Question 1

Correct Answer:

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Look for marks assuring parallelism.

How many reflection symmetries does a right circular cylinder have?

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Question 2

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Infinitely many (for example, any plane through the centers of the bases, or any plane containing the line through the two centers)

With a compass and a straightedge, construct a rectangle having sides with these two lengths: 3 inches and 4 inches. Do not erase any key construction marks.

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Question 3

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Look for marks that would assure a rectangle. These might not reflect the official definition of a rectangle as a parallelogram with right angles, so the follow-up discussion could pursue the other methods.

Given the circle with center O shown, give an example of the following. A) a minor arc B) a major arc C) a diameter D) Draw a chord and label it AB. E) Shade in a sector.

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Question 4

Prism is to pyramid as cylinder is to _____.

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Question 5

Explain how the mathematical ideas of "cylinder" and "cone" are different from most people's traditional, everyday use of these terms.

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Question 6

Give the sizes of the lettered angles in the following figure. Do not forget to give the units.

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Question 7

Tell whether each statement is always true, sometimes true, or never true. Support your decisions. A) A chord of a circle may have one endpoint at the center of the circle. B) An oblique circular cylinder has reflection symmetry.

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Question 8

Are the following statements true or false?

Every chord of a circle is a diameter of a circle.

True

The diameter of a circle is the longest chord of a circle.

False

Correct Answer:

Verified

Every chord of a circle is a diameter of a circle.

The diameter of a circle is the longest chord of a circle.

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Question 9

Using a compass and a straightedge, construct an isosceles trapezoid that is not equiangular. Do not erase any important construction marks.

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Question 10

Is the following statement always true, sometimes true, or never true? Explain. A diameter is a chord of the circle.

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Question 11

With a compass and a straightedge, construct an angle of 135°. (Hint: 135 = 90 + …)

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Question 12

A) Draw a segment of any length and label it GR. Copy segment GR using a compass and a straightedge. Call it JM. Show all construction marks. B) Construct the perpendicular bisector of line segment GR. Show all construction marks.

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Question 13

Draw, as carefully as possible, the following figures. A) a right circular cone B) an oblique elliptical cylinder

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Question 14

Are the following statements true or false?

Every two spheres are similar.

False

A chord is a diameter.

True

If Earth were a perfect sphere, then the equator would be considered a minor circle.

Correct Answer:

Verified

Every two spheres are similar.

A chord is a diameter.

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Question 15

A) Draw an angle of any size and label it O. Copy angle O using a compass and a straightedge. Call it P. Show all construction marks. B) Construct the angle bisector of angle O. Show all construction marks.

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Question 16

Draw an acute angle and label it O. With a compass and a straightedge (and without a protractor), construct an angle with a size 1.5 times the size of angle O. Do not erase any key construction marks.

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Question 17

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Exam 21: Curves, Constructions, and Curved Surfaces

Draw a line m and a point P not on the line. With a compass and a straightedge, construct a line through point P that is parallel to line m. Do not erase any key construction marks.

How many reflection symmetries does a right circular cylinder have?

With a compass and a straightedge, construct a rectangle having sides with these two lengths: 3 inches and 4 inches. Do not erase any key construction marks.

Given the circle with center O shown, give an example of the following. A) a minor arc B) a major arc C) a diameter D) Draw a chord and label it AB. E) Shade in a sector.

Prism is to pyramid as cylinder is to _____.

Explain how the mathematical ideas of "cylinder" and "cone" are different from most people's traditional, everyday use of these terms.

Give the sizes of the lettered angles in the following figure. Do not forget to give the units.

Tell whether each statement is always true, sometimes true, or never true. Support your decisions. A) A chord of a circle may have one endpoint at the center of the circle. B) An oblique circular cylinder has reflection symmetry.

Using a compass and a straightedge, construct an isosceles trapezoid that is not equiangular. Do not erase any important construction marks.

Is the following statement always true, sometimes true, or never true? Explain. A diameter is a chord of the circle.

With a compass and a straightedge, construct an angle of 135°. (Hint: 135 = 90 + …)

A) Draw a segment of any length and label it GR. Copy segment GR using a compass and a straightedge. Call it JM. Show all construction marks. B) Construct the perpendicular bisector of line segment GR. Show all construction marks.

Draw, as carefully as possible, the following figures. A) a right circular cone B) an oblique elliptical cylinder

A) Draw an angle of any size and label it O. Copy angle O using a compass and a straightedge. Call it P. Show all construction marks. B) Construct the angle bisector of angle O. Show all construction marks.

Draw an acute angle and label it O. With a compass and a straightedge (and without a protractor), construct an angle with a size 1.5 times the size of angle O. Do not erase any key construction marks.

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Meanings for Fractions

Computing With Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Transformation Geometry

Measurement Basics

Area, Surface Area, and Volume

Counting Units Fast: Measurement Formulas

Special Topics in Measurement

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

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