Section 1
Representations of Three-Dimensional Figures
Sketch a rectangular prism 4 units high, 2 units long, and 3 units wide using isometric dot paper.(FIGURE CAN'T COPY)
Draw a corner view of the figure given its orthographic drawing.(FIGURE CAN'T COPY)
A deli slicer is used to cut cylindrical blocks of cheese for sandwiches. Suppose a customer wants slices of cheese that are round and slices that are rectangular. How can the cheese be placed on the slicer to get each shape?
Sketch each solid using isometric dot paper.rectangular prism 3 units high, 4 units long, and 5 units wide
Sketch each solid using isometric dot paper.cube 5 units on each edge
Sketch each solid using isometric dot paper.cube 4 units on each edge
Sketch each solid using isometric dot paper.rectangular prism 6 units high, 6 units long, and 3 units wide
Sketch each solid using isometric dot paper.triangular prism 4 units high, with bases that are right triangles with legs 5 units and 4 units long
Sketch each solid using isometric dot paper.triangular prism 2 units high, with bases that are right triangles with legs 3 units and 7 units long
Draw a corner view of a figure given each orthographic drawing.(FIGURE CAN'T COPY)
Determine the shape resulting from each cross section of the cone.(FIGURE CAN'T COPY)
Determine the shape resulting from each cross section of the rectangular prism.(FIGURE CAN'T COPY)
Draw a diagram and describe how a plane can slice a tetrahedron to form the following shapes.equilateral triangle
Draw a diagram and describe how a plane can slice a tetrahedron to form the following shapes.isosceles triangle
Draw a diagram and describe how a plane can slice a tetrahedron to form the following shapes.quadrilateral
A well-cut diamond enhances the natural beauty of the stone. These cuts are called facets. Describe the shapes seen in an uncut diamond.
Many minerals have a crystalline structure. The forms of three minerals are shown below. Describe the cross sections from a horizontal and vertical slice of each crystal.(FIGURE CAN'T COPY)
Given the net of a solid, use isometric dot paper to draw the solid.(FIGURE CAN'T COPY)
Given the corner view of a figure, sketch the orthographic drawing.(FIGURE CAN'T COPY)
Given the corner view of a figure, sketch the orthographic drawing.
In a two-dimensional plane, figures are symmetric with respect to a line or a point. In three-dimensional space, solids are symmetric with respect to a plane. This is called reflection symmetry. A square pyramid has four planes of symmetry. Two pass through the altitude and one pair of opposite vertices of the base. Two pass through the altitude and the midpoint of one pair of opposite edges of the base.For each solid, determine the number of planes of symmetry and describe them.tetrahedron
In a two-dimensional plane, figures are symmetric with respect to a line or a point. In three-dimensional space, solids are symmetric with respect to a plane. This is called reflection symmetry. A square pyramid has four planes of symmetry. Two pass through the altitude and one pair of opposite vertices of the base. Two pass through the altitude and the midpoint of one pair of opposite edges of the base.For each solid, determine the number of planes of symmetry and describe them.cylinder
In a two-dimensional plane, figures are symmetric with respect to a line or a point. In three-dimensional space, solids are symmetric with respect to a plane. This is called reflection symmetry. A square pyramid has four planes of symmetry. Two pass through the altitude and one pair of opposite vertices of the base. Two pass through the altitude and the midpoint of one pair of opposite edges of the base.For each solid, determine the number of planes of symmetry and describe them.sphere
Three-dimensional solids exhibit rotational symmetry in the same way as two-dimensional figures. Identify the order and magnitude of the rotational symmetry of each solid with respect to its base.regular pentagonal prism
Three-dimensional solids exhibit rotational symmetry in the same way as two-dimensional figures. Identify the order and magnitude of the rotational symmetry of each solid with respect to its base.tetrahedron
The cross section of a solid is an octagon. Name the solids that have octagonal cross sections.
REASONING Of the two-dimensional representations that you have studied, which would you choose to represent plans for a new skyscraper? Explain.
Select three different three-dimensional figures. Draw a net for each on cardboard. Cut out the cardboard and use tape to construct each model.
Identify the term that does not belong with the other three. Explain your reasoning.isometric drawing net $\quad$ construction orthographic drawing
Analyze the relationship between a three-dimensional solid and a two-dimensional representation. Include a description of orthographic drawings and isometric drawings.
Which of the following cannot be formed by the intersection of a cube and a plane?$\mathbf{A}$ a triangle$\mathbf{B}$ a rectangle$\mathbf{C}$ a point$\mathbf{D}$ a circle
How many centimeters are in 35 millimeters?F. 0.35 centimetersG. 3.5 centimetersH. 350 centimetersJ. $35,000$ centimeters
The results of a restaurant survey are shown in the circle graph with the measurement of each central angle. Each customer was asked to choose a favorite entrée. If a customer is chosen at random, find the probability of each response.(PIE GRAPH CAN'T COPY)steak
The results of a restaurant survey are shown in the circle graph with the measurement of each central angle. Each customer was asked to choose a favorite entrée. If a customer is chosen at random, find the probability of each response.(PIE GRAPH CAN'T COPY)not seafood
The results of a restaurant survey are shown in the circle graph with the measurement of each central angle. Each customer was asked to choose a favorite entrée. If a customer is chosen at random, find the probability of each response.(PIE GRAPH CAN'T COPY)either pasta or chicken
The results of a restaurant survey are shown in the circle graph with the measurement of each central angle. Each customer was asked to choose a favorite entrée. If a customer is chosen at random, find the probability of each response.(PIE GRAPH CAN'T COPY)neither pasta nor steak
The coordinates of the vertices of a composite figure are given. Find the area of each figure. $$A(1,4), B(4,1), C(1,-2), D(-3,1)$$
The coordinates of the vertices of a composite figure are given. Find the area of each figure. $$F(-2,-4), G(-2,-1), H(1,1), J(4,1), K(6,-4)$$
Solve each $\triangle A B C$ described below. Round to the nearest tenth if necessary. $$m \angle A=54, b=6.3, c=7.1$$
Solve each $\triangle A B C$ described below. Round to the nearest tenth if necessary. $$m \angle B=47, m \angle C=69, a=15$$
Determine the relationship between the measures of the given angles. (DIAGRAM CAN'T COPY)$$\angle A D B, \angle A B D$$
Determine the relationship between the measures of the given angles. (DIAGRAM CAN'T COPY)$$\angle A B D, \angle B A D$$
Determine the relationship between the measures of the given angles. (DIAGRAM CAN'T COPY)$$\angle B C D, \angle C D B$$
Determine the relationship between the measures of the given angles. (DIAGRAM CAN'T COPY)$$\angle C B D, \angle B C D$$
Find the area of each figure.(FIGURE CAN'T COPY)