Deck 21: Curves, Constructions, and Curved Surfaces

Question 1

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

Answer 1

The usage in mathematics allows different bases, whereas everyday usage is likely restricted to right circular cylinders and cones. Answers can vary.

Question 2

Draw, as carefully as possible, the following figures.

A) a right circular cone
B) an oblique elliptical cylinder

Answer 2

Check that drawings meet the described figures.

Question 3

Prism is to pyramid as cylinder is to _____.

Answer 3

cone

Question 4

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.

Question 5

How many reflection symmetries does a right circular cylinder have?

Question 7

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

Question 9

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.

Question 10

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

Question 11

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.

Question 12

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.

Question 13

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.

Question 14

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

Question 15

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.

Question 16

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.

Question 17

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