Warm Up Use the linking cubes to create each figure from Exploration 8.17. As a group, check your answers! How close were you???

Agenda Go over warm up Pyramids, Prisms, and other solids Begin Transformations Exploration 9.1 Exploration 9.5 Exploration 9.6 Assign Homework

Try these other two Front Right Side Top

Draw the views Front Right Side Top

Nets When we think of polyhedra, we think of the 3-dimensional figure. If we wanted to find the surface area, it would help if we could spread it out and look at it in 2-dimensions. To do this, we find the net of the polyhedron.

Nets Exploration 8.19 Part 3 Examine each of the nets. Without cutting or folding, determine the type of 3-dimensional figure it will create. Last, draw another net that will create the same 3-dimensional figure. If it is not possible, explain why not.

Solids Prisms: cubes, rectangular, triangular, etc… A polyhedron and its interior. Named for their bases. A triangular prism has 2 bases that are triangles. Top and bottom bases are parallel and congruent. Faces are all rectangles with the same height.

Solids Cylinders: Like prisms, but with 2 bases that are circles. One other face in the shape of a rectangle.

Solids Pyramids: square, triangular, hexagonal, etc. Named for the base. Has just one base, and the other faces are triangles. The height of the triangle faces is called the slant height.

Solids Cones: Like pyramids, but with a circular base. Face is a sector of a circle. Top point is called an apex. Spheres: No faces or bases. “Equator” is known as a great circle.

We can transform shapes Given (preimage) Transformed:(image)

General Notes Preimage: what you start with Image: what you end up with after a transformation. Transformations that yield congruence: reflection, rotation, translation (flips, turns, and slides) If a figure has only 180˚ rotation symmetry, we say it has point symmetry. Order makes a difference: e.g., doing 2 different reflections in a row in the opposite order may not give the same image.

Reflections Miras Look at it--there are two sides. Flat edge on line of reflection towards pre-image, indented edge toward image. Look through to find reflection.

Exploration 9.4 Do part 1 like this in pairs: Go through 1a - c, and mark where you predict the image to be. Check with the Mira. Then, do 1d - f, and mark where you predict the image to be. Repeat this process for 3a - c, and d - f.

Now, use a ruler… Measure the perpendicular distance from any preimage point to the line of reflection: compare this distance to its respective image point and the line of reflection. The line of reflection is _____ of the segment containing any preimage and its respective image.

More advanced Take out the worksheet Practice Using Miras. (It is on the flip side of your Quadrilateral Hierarchy worksheet.) In your groups, first discuss HOW you will find each of these. Then, individually, try it. Compare answers, revise, and then repeat.

Exploration 9.5 Paper folding--in pairs: your goal is to do Part 2 a - h. Do as many as you need in order to write directions for a student to determine what the unfolded paper will look like based on the folded paper diagram.

Exploration 9.6 On your own, make predictions for the images of a - i when a 180˚ rotation is made. Then, use patty paper to check your work. Then, use a different color and determine the preimage for a 90˚ clockwise rotation.