Geometry Cakes and Pancakes

4.2 Translating and Stacking Two-Dimensional Figures Objectives Apply translations to two-dimensional plane figures to create three-dimensional solids Describe three-dimensional solids formed by translations of plane figures through space Build three-dimensional solids by stacking congruent or similar two-dimensional plane figures

Problem 1 These Figures Take the Cake Together #1 Each Lateral Face is a rectangle The solid is a triangular prism Has 2 bases that are triangles Isometric Paper = Dot Paper

Problem 1 These Figures Take the Cake Individually draw all of #2 Use a straightedge When finished drawing, Collaborate #3 Total Time: 5 Minutes

Problem 1 These Figures Take the Cake Right Triangular Prism Formed when a triangle has been translated through space in a direction that is perpendicular to the plane Oblique Triangular Prism Formed when a triangle has been translated through space in a direction that is NOT perpendicular to the plane

Problem 1 These Figures Take the Cake Together #4 and #5 The shape of the face of an oblique triangular prism is a parallelogram The shape of each lateral face is a rectangle The name of the figure formed is a rectangular prism There are 2 bases in the shape of rectangles

Problem 1 These Figures Take the Cake Collaborate 6-7 (5 Minutes)

Problem 1 These Figures Take the Cake Right Rectangular Prism Formed when a rectangle has been translated through space in a direction that is perpendicular to the plane Oblique Rectangular Prism Formed when a rectangle has been translated through space in a direction that is NOT perpendicular to the plane

Problem 1 These Figures Take the Cake Together 8-12 The shape of the face of an oblique rectangular prism is a parallelogram The shape of each lateral face is a rectangle The name of the figure formed is a cylinder There are 2 bases in the shape of circles

Problem 1 These Figures Take the Cake

Problem 1 These Figures Take the Cake Right Cylinder Formed when a circle has been translated through space in a direction that is perpendicular to the plane Oblique Cylinder Formed when a circle has been translated through space in a direction that is NOT perpendicular to the plane

Problem 1 These Figures Take the Cake Together 13-14 The shape of the lateral face is a parallelogram

Problem 2: Congruent and Similar Collaborate 1-4 (4 Minutes) Together #5 The solid that is formed by stacking the polygons is a Right (Shape of the Base) Prism

Problem 2: Congruent and Similar Collaborate 6-11 (Rest of Class: No HW) Page 312 #11 Prisms To find the area of the base of the prism, we use the area formula for that particular shape The height of the prism is the height of the stack Volume of a prism would be the area of the base x height #11 Cylinders To find the area of the base of the cylinder, we use the area formula for a circle (𝜋 𝑟 2 ) The height of the cylinder is the height of the stack Volume of a cylinder would be the area of the base x height Together #12

Prisms Pyramids Cylinders Cones 𝑉= 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡 𝑉=𝐵ℎ 𝑉= 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡 𝑉=𝐵ℎ Translating Polygons Stacking Polygons Pyramids 𝑉= 1 3 𝐵ℎ Stacking Similar Polygons Volume Formulas and Transformations Cylinders 𝑉=𝜋 𝑟 2 ℎ Translating Circles Rotating Rectangles Stacking Circles Cones 𝑉= 1 3 𝜋 𝑟 2 ℎ Rotating a Right Triangle Stacking Similar Circles

Talk the Talk Pg. 315 Instead of cutting out the pieces, we will discuss which shapes are formed by the actions in the boxes Sphere / Cone / Cylinder / Pyramid / Prism We will work top to bottom then move over

Prism Prism Prism Prism Cylinder Cylinder Cone Sphere Cylinder Cone Sphere Prism Pyramid Prism Pyramid Prism Pyramid

Formative Assessment Skills Practice 4.2 Vocabulary Pg. 423 (1-7) Matching Problem Set Pg. 424-428 (1-24)