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Pythagorean Theorem and 3-D Figures

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Pythagorean Theorem and 3-D Figures

- Every rectangular solid has:
- 6 rectangular faces:
- 1.
- 2.
- 3.
- 4.
- 5.
- 6.

- 12 edges:
- 1. 2.
- 3. 4.
- 5. 6.
- 7. 8.
- 9. 10.
- 11. 12.

- 4 diagonals:
- 1.
- 2.
- 3.
- 4.
- A cube is a rectangular solid in which all edges are congruent. All faces are squares!

- KLQP is a square and is called the base.
- J is the vertex.
- is the altitude of the pyramid and is perpendicular to the base at its center.
- is called the slant height and is perpendicular to a side of the base.

- If BC = 3, what is AD?
- If AB = 4 what is DB?
- Must use BC = 3 to find
- If CG =12, what is DH?
- What is BH? AG?
- Use DB = 5

- The dimensions of a rectangular solid are 3, 5, and 7. Find the diagonal.
- Draw a rectangular solid.
- Does it matter where the numbers go?
- 1st possibility
- Find AH
- To find AH first must find DH
- Use DH to find AH

- 2nd possibility
- Find AH
- To find AH first must find DH
- Use DH to find AH

- 3rd possibility
- Find AH
- To find AH first must find DH
- Use DH to find AH

- The square pyramid has altitude , slant height , perimeter of JKMO = 40, and PK = 13.
- Find
- a.) JK
- Since it is a square pyramid,
- the base is a square
- A square has 4 congruent sides
- If the perimeter is 40 then each
- side is 10 so JK = 10

- b.) PS
- In a square pyramid, the slant
- height bisects the base edge
- So KS = 5
- Use PK = 13 to find PS
- PS = 12

- C.) PR
- In a square pyramid, the altitude
- height bisects the base edge
- So RS = 5
- Use PS = 12 to find PR

- With any type of solid, you need to create right triangles that you can use the Pythagorean to find the missing length.
- You may need to use the Pythagorean theorem more than once to find the missing length.