Geometry – Chapter 12 Lesson Plans
Section 12.1–Solid Figures
Enduring Understandings: The student shall be able to:
- Identify solid figures.
Standards:
35. Perimeter, Area, and Volume
Identifies polyhedrons, including prisms, pyramids, cubes, and tetrahedrons; cylinders; cones; spheres; faces; edges; vertices; bases; and lateral edges.
Essential Questions: How do we identify solid shapes?
Warm up/Opener:
Activities:
Solid Figures are figures that enclose a part of space.
Polyhedrons are solids with flat surfaces that are polygons.
Faces are the two dimensional surfaces formed by the polygons and their interiors.
A vertex is where three or more edges intersect at a point.
Two faces intersect in a segment called an edge.
Make some shapes and have students identify the above vocabulary words.
Prisms and pyramids are two types of polyhedrons.
A prism has two parallel congruent faces called bases connected by lateral faces, which are parallelograms. Each pair of adjacent lateral faces has a common lateral edge. The lateral edges are parallel segments.
A pyramid has one face that is called the base. All the other faces intersect at a common point called the vertex. The faces that meet are called lateral faces, and they are all triangles. The edges of the lateral faces that have the vertex as an endpoint are called lateral edges. The altitude is the segment from the vertex perpendicular to the base.
Prisms and pyramids are classified by the shape of their bases. See the shapes on page 497. Talk about triangular rectangular, hexagonal, etc. prisms and pyramids. Talk about a cube being a special rectangular prism, and that tetrahedron is another name for triangular pyramid, and that all its faces are triangles.
Cylinders have two circular bases and a lateral curved surface.
Cones have a single circular base and the lateral surface is curved. The point of the cone is called a vertex. The axis of the cone is from the center of the base to the vertex. The height is the perpendicular distance from the plane of the base to the vertex.
Cylinders and cones have one and two bases respectively, but are not polyhedrons. Why? Faces are not polygons.
Talk about the shapes created by slicing through various shapes, such as a cylinder, cube, prism, or pyramid.
Problem 33 on page 501: “Discover” Euler’s Formula (V + F – 2 = E) by looking at triangular and rectangular prisms and pyramids and a pentagonal prism.
Talk about orthographic drawings (sometimes referred to as engineering drawings) show the front, top, and right side view of an object. The shape can also be drawn using isometric paper, where the lines are at 30 angles.
A polyhedron is regular if all of its faces are shaped like congruent regular polygons. Since all of the faces of a regular polyhedron are regular and congruent, all of the edges of a regular polyhedron are congruent. There are exactly five types of regular polyhedra. These are called Platonic Solids, because Plato described them so fully in his writings. They are:
Name / # of Faces / Shape of FacesTetrahedron / 4 / Triangle
Octahedron / 8 / Triangle
Hexahedron / 6 / Square
Dodecahedron / 12 / Pentagon
.Icosahedron / 20 / Triangle
NOTE: A capsid is the protein shell of a virus. Capsids are broadly classified according to their structure. The majority of viruses have capsids with either helical or icosahedral structure. The icosahedral shape, which has 20 equilateral triangular faces, approximates a sphere, while the helical shape is cylindrical. (Wikipedia, capsid)
Assessments:
Do the “Check for Understanding” 2, 3-9
CW WS 12-1
HW pg 499 – 501, # 15 - 39odd,(13)
HW 12-1 Enrichment – to be done later, after EOCT