Name the shape of the base of the following prisms: Rectangular prism Triangular prism

1. Name the shape of the base of the following prisms: Rectangular prism Triangular prism Hexagonal prism Pentagonal prism Octagonal prism How many faces of the figures above have the same shape as the base? If you cut a shape parallel to its base, what shape does it take? If you cut a shape perpendicular to its base, what shape does it take? http://www.learner.org/courses/learningmath/geometry/session9/solutions_c.html#c1

2. 3-25-13 Cross Sections EQ: What is a cross section? How many different two-dimensional figures can you make by slicing a cube? How can you use cross sections to help identify solids? BOP Name the shape of the base of the following prisms: Rectangular prism Triangular prism Hexagonal prism Pentagonal prism Octagonal prism How many faces of the figures above have the same shape as the base?

3. Match the Cross Sectional Views with the 3D figures:

6. X rays, MRI’s and CAT scans help medical doctors make accurate diagnoses. These images show cross sections of the parts of the human body that Physicians want to investigate.

7. CAT SCAN MACHINE

9. Cross Sections • A cross section is the shape you get when cutting straight across an object.

10. Cross section of a tree stump

11. Scan of abdominal area

12. Heart Scan

13. What cross section can you get from each of these figures?

14. What is the top view of a globe (sphere) cut at the equator? cut just below the north pole?

19. If a cone is sliced parallel to the base, what will the cross-sections look like? What if the cut is perpendicular to its base?

20. What is a cross section? • In geometry it is the shape made when a solid is cut through parallel to the base. • Note: don't draw the rest of the object, just the shape made when you cut through.

21. Cross SectionBelow are three cross sections of a pyramid with a square base: Cross Sections of a Pyramid

24. CROSS SECTION OF A RECTANGULAR PRISM Notice how the cross section is shaded.

25. Triangular Prism

26. How many 2D figures can you make by taking cross sections of a cube? Use isometric dot paper to draw a cube. Make each face 3 dots X 3 dots. Inside the cube, shade in the cross section with colored pencils.

27. Try to make the following cross sections by slicing a cube: Hint: How may faces does a cube have? Each cross section comes from cutting through a face of your cube. 

28. A square cross section can be created by slicing the cube by a plane parallel to one of its sides.

29. An equilateral triangle cross section can be obtained by cutting the cube by a plane defined by the midpoints of the three edges coming from any one vertex.

30. SOLUTIONS One way to obtain a rectangle that is not a square is by cutting the cube with a plane perpendicular to one of its faces (but not perpendicular to the edges of that face), and parallel to the four, in this case, vertical edges

31. Pick a vertex, let's say A, and consider the three edges meeting at the vertex. Construct a plane that contains a point near a vertex (other than vertex A) on one of the three edges, a point in the middle of another one of the edges, and a third point that is neither in the middle nor coinciding with the first point. Slicing the cube with this plane creates a cross section that is a triangle, but not an equilateral triangle; it is a scalene triangle. Notice that if any two selected points are equidistant from the original vertex, the cross section would be an isosceles triangle.

32. To get a pentagon, slice with a plane going through five of the six faces of the cube.

33. To create a non-rectangular parallelogram, slice with a plane from the top face to the bottom. The slice cannot be parallel to any side of the top face, and the slice must not be vertical. This allows the cut to form no 90° angles. One example is to cut through the top face at a corner and a midpoint of a non-adjacent side, and cut to a different corner and midpoint in the bottom face.

34. To get a hexagon, slice with a plane going through all six faces of the cube. It is not possible to create a circular cross section or an octagonal cross section of a cube.

35. Summary: What can a cross section tell you about a solid? What information are you missing when you look at a cross section? When and how are cross sections used in real life?