Draw isometric views of three-dimensional figures. Investigate cross sections of three- dimensional figures. Splash Screen

Mathematical Practices 5 Use appropriate tools strategically. Content Standards G.GMD.4 Identify the shapes of two- dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects. Mathematical Practices 5 Use appropriate tools strategically. 1 Make sense of problems and persevere in solving them. CCSS

isometric view cross section Vocabulary

Vocabulary

Use Dimensions of a Solid to Sketch a Solid Use isometric dot paper to sketch a triangular prism 6 units high, with bases that are right triangles with legs 6 units and 4 units long. Step 1 Mark the corner of the solid, then draw segments 6 units down, 6 units to the left, and 4 units to the right. Example 1

Step 2 Draw the triangle for the top of the solid. Use Dimensions of a Solid to Sketch a Solid Step 2 Draw the triangle for the top of the solid. Example 1

Use Dimensions of a Solid to Sketch a Solid Step 3 Draw segments 6 units down from each vertex for the vertical edges. Example 1

Use Dimensions of a Solid to Sketch a Solid Step 4 Connect the corresponding vertices. Use dashed lines for the hidden edges. Shade the top of the solid. Answer: Example 1

Which diagram shows a rectangular prism 2 units high, 5 units long, and 2 units wide? A. B. C. D. Example 1

Use an Orthographic Drawing to Sketch a Solid Use isometric dot paper and the orthographic drawing to sketch a solid. The top view indicates one row of different heights and one column in the front right. Example 2

Use Dimensions of a Solid to Sketch a Solid The front view indicates that there are four standing columns. The first column to the left is 2 blocks high, the second column is 3 blocks high, the third column is 2 blocks high, and the fourth column to the far right is 1 block high. The dark segments indicate breaks in the surface. The right view indicates that the front right column is only 1 block high. The dark segments indicate a break in the surface. Example 2

The left view indicates that the back left column is 2 blocks high. Use Dimensions of a Solid to Sketch a Solid The left view indicates that the back left column is 2 blocks high. Draw the figure so that the lowest columns are in front and connect the dots on the isometric dot paper to represent the edges of the solid. Answer: Example 2

top view left view front view right view Which diagram is the correct corner view of the figure given the orthographic drawing? A. B. C. D. Example 2

Example 3

Identify Cross Sections of Solids BAKERY A customer ordered a two-layer sheet cake. Determine the shape of each cross section of the cake below. Example 3

Identify Cross Sections of Solids Answer: If the cake is cut horizontally, the cross section will be a rectangle. If the cake is cut vertically, the cross section will also be a rectangle. Example 3

Homework Page 841 (8-14 Even, 16-19, 25-27) Example 3