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Sketch a solid with a uniform cross-section ABCDE and edge BH. Indicate hidden edges with broken lines and visible edges with solid lines.

Mathematics

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Answer

To complete the sketch of the solid with a uniform cross-section ABCDE and edge BH, we need to draw the remaining edges, indicating hidden edges with broken lines and visible edges with solid lines.

Step-by-step solution

3 steps
  1. Identify the corresponding points for A, C, D, E on the back face.

    Since BH is an edge, H is the point corresponding to B on the back face. We will label the points corresponding to A, C, D, E as A', C', D', E' respectively.

  2. Draw the edges connecting the front face to the back face.

    These edges will be parallel to BH and have the same length as BH.

    • Draw a line segment from A, parallel to BH, to point A'. This line segment AA' will be hidden, so draw it as a broken line.
    • Draw a line segment from C, parallel to BH, to point C'. This line segment CC' will be visible, so draw it as a solid line.
    • Draw a line segment from D, parallel to BH, to point D'. This line segment DD' will be visible, so draw it as a solid line.
    • Draw a line segment from E, parallel to BH, to point E'. This line segment EE' will be hidden, so draw it as a broken line.
  3. Draw the edges of the back face (A'HC'D'E').

    • Draw a line segment connecting A' to H. This line segment A'H will be hidden, so draw it as a broken line.
    • Draw a line segment connecting H to C'. This line segment HC' will be visible, so draw it as a solid line.
    • Draw a line segment connecting C' to D'. This line segment C'D' will be visible, so draw it as a solid line.
    • Draw a line segment connecting D' to E'. This line segment D'E' will be visible, so draw it as a solid line.
    • Draw a line segment connecting E' to A'. This line segment E'A' will be hidden, so draw it as a broken line.

    The completed sketch will show the original pentagon ABCDE and the line BH as solid lines. The additional lines will be:

    • Broken lines: AA', EE', A'H, E'A'
    • Solid lines: CC', DD', HC', C'D', D'E'

    The final answer is the completed sketch as described above.

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