# Pythagorean Theorem and 3-D Figures - PowerPoint PPT Presentation

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Pythagorean Theorem and 3-D Figures. Rectangular solids. 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.

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Pythagorean Theorem and 3-D Figures

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## Pythagorean Theorem and 3-D Figures

### Rectangular solids

• 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!

### Regular Square Pyramid

• 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.

### Example 1: This box is a rectangular solid.

• 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

### Example 2:

• 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

### Example 2:

• 2nd possibility

• Find AH

• To find AH first must find DH

• Use DH to find AH

### Example 2:

• 3rd possibility

• Find AH

• To find AH first must find DH

• Use DH to find AH

### Example 3:

• 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

### In review,

• 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.