











Lesson 12.1 Nets & Platonic Solids 




In this lesson students will:
 understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders
 identify the vertices, edges, and faces of polyhedra
 identify polygons of polyhedra represented by nets
 use nets to create the five Platonic solids
 create nets for polyhedra
Essential Ideas:
 A polyhedron is a threedimensional solid formed by polygons that enclose a region.
 The face of a polyhedron is one of the polygons forming the solid. The bases of a polyhedron are the faces on the top and bottom of the polyhedron. The lateral face of a polyhedron is any face that is not a base.
 An edge of a polyhedron is the segment formed by the intersection of two faces.
 A vertex of a polyhedron is the point of intersection of three or more edges.
 A regular polyhedron is a threedimensional solid formed by congruent regular polygons.
 The five Platonic solids are tetrahedon (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces).
 A net is a twodimensional representation of the faces of a polyhedron.
















Lesson 7.4 Angles of Elevation, Angles of Depression, and Equivalent Trigonometric Ratios 




In this lesson students will:
 use trigonometric ratios to solve for the angle of elevation
 use trigonometric ratios to solve for the angle of depression
 discover equivalent trigonometric ratios
Essential Ideas:
An angle of elevation is the angle above the horizontal.
An angle of depression is the angle below the horizontal.
A clinometer is an instrument used to measure angles of elevation and angles or depression.
In right triangles where angle A and angle B are the acute angles, the equivalent trigonometric ratios are:
sin A = cos B
cos A = sin B
tan A = cot B
csc A = sec B
sec A = csc B
cot A = tan B



