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12-1 Representations of ThreeDimensional Figures You identified parallel planes and intersecting planes in three dimensional figures. • Draw isometric views of three-dimensional figures. • Investigate cross sections of threedimensional figures. Vocabulary Isometric view: corner views of three dimensional objects on two-dimensional paper. Orthographic drawing: a drawing showing the top, left, front, and right views of 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. Step 2 Draw the triangle for the top of the solid. Step 3 Draw segments 6 units down from each vertex for the vertical edges. Step 4 Connect the corresponding vertices. Use dashed lines for the hidden edges. Shade the top of the solid. Answer: Which diagram shows a rectangular prism 2 units high, 5 units long, and 2 units wide? A. B. C. D. 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. 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. 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 Which diagram is the correct corner view of the figure given the top left fron righ orthographic drawing? view view t t view view A. B. C. D. Cross Section A cross section: the intersection of a solid and a plane. The shape of the cross section formed by the intersection of a plane and a three-dimensional figure depends on the angle of the plane. BAKERY A customer ordered a two-layer sheet cake. Determine the shape of each cross section of the cake below. 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. 12-1 Assignment Page 841, 8-13, 16-20