Questions: BUILDING The roof and exterior walls of a house represent intersecting planes. Using the image, name all the lines that are formed by the intersecting planes. O C, A D, A F, G E, G D, B C, C E A B, A G, A H, B C, B H, C D, D E, D H, E F, F G, F H E G, D A, C A, F B, E C, D H, C B A B, A D, A E, B C, B H, C D, D A, C A, E F, E G, E H

BUILDING The roof and exterior walls of a house represent intersecting planes. Using the image, name all the lines that are formed by the intersecting planes. O C, A D, A F, G E, G D, B C, C E A B, A G, A H, B C, B H, C D, D E, D H, E F, F G, F H E G, D A, C A, F B, E C, D H, C B A B, A D, A E, B C, B H, C D, D A, C A, E F, E G, E H
Transcript text: BUILDING The roof and exterior walls of a house represent intersecting planes. Using the image, name all the lines that are formed by the intersecting planes. $\overleftrightarrow{O C}, \overleftrightarrow{A D}, \overleftrightarrow{A F}, \overleftrightarrow{G E}, \overleftrightarrow{G D}, \overleftrightarrow{B C}, \overleftrightarrow{C E}$ $\overleftrightarrow{A B}, \overleftrightarrow{A G}, \overleftrightarrow{A H}, \overleftrightarrow{B C}, \overleftrightarrow{B H}, \overleftrightarrow{C D}, \overleftrightarrow{D E}, \overleftrightarrow{D H}, \overleftrightarrow{E F}, \overleftrightarrow{F G}, \overleftrightarrow{F H}$ $\overleftrightarrow{E G}, \overleftrightarrow{D A}, \overleftrightarrow{C A}, \overleftrightarrow{F B}, \overleftrightarrow{E C}, \overleftrightarrow{D H}, \overleftrightarrow{C B}$ $\overleftrightarrow{A B}, \overleftrightarrow{A D}, \overleftrightarrow{A E}, \overleftrightarrow{B C}, \overleftrightarrow{B H}, \overleftrightarrow{C D}, \overleftrightarrow{D A}, \overleftrightarrow{C A}, \overleftrightarrow{E F}, \overleftrightarrow{E G}, \overleftrightarrow{E H}$
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Solution

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Solution Steps

Step 1: Identify the Intersecting Planes
  • The roof and exterior walls of the house represent intersecting planes. We need to identify the lines formed by these intersections.
Step 2: List the Intersecting Lines
  • The lines formed by the intersecting planes are the edges of the house. These edges are:
    • AB, AD, AE, BC, CD, DA, CA, EF, EG, EH, and GH.
Step 3: Match the Correct Option
  • Compare the listed lines with the given options:
    • Option A: AC, AD, AE, BC, CD, DA, CA, EF, EG, EH
    • Option B: AB, AD, AE, BC, CD, DA, CA, EF, EG, EH
    • Option C: AB, AD, AE, BC, CD, DA, CA, EF, EG, EH
    • Option D: AB, AD, AE, BC, CD, DA, CA, EF, EG, EH

Final Answer

  • The correct option is Option D: AB, AD, AE, BC, CD, DA, CA, EF, EG, EH.
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