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10­3 Smart Board Notes Day 1 Petre.notebook
Fun Facts of the Day
The most common name in the
world is _____________
The youngest Pope of the
catholic church was
_____ years old
Holt Geometry
We will learn about a very
famous mathematician,
Leonard Euler
For Day 1, you will need:
* Isometric dot paper
* Calculator
Holt Geometry
A polyhedron is formed by polygons that intersect only at their edges. Prisms and pyramids are polyhedrons, but cylinders and cones are not.
How would you describe the difference?
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10­3 Smart Board Notes Day 1 Petre.notebook
Leonard Euler
pronounced “Oiler”
(1707­1783)
Euler’s Formula: The relationship between the vertices, edges, and faces of a polyhedron
Example 1A: Using Euler’s Formula
Find the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula.
Example 1B: Using Euler’s Formula
Find the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula.
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10­3 Smart Board Notes Day 1 Petre.notebook
A diagonal of a three­dimensional figure connects
two vertices of two different faces. Diagonal d of a rectangular prism is shown in the diagram.
Example 2A: Using the Pythagorean Theorem in Three Dimensions
Find the length of the diagonal of a 6 cm by 8 cm by 10 cm rectangular prism
Example 2B: Using the Pythagorean Theorem in Three Dimensions
Find the height of a rectangular prism with a 12 in. by 7 in. base and a 15 in. diagonal
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10­3 Smart Board Notes Day 1 Petre.notebook
Space is the set of all points in three dimensions.
Three coordinates are needed to locate a point in space. A three­dimensional coordinate system has 3 perpendicular axes: the x­axis, the y­axis, and the z­axis. An ordered triple (x, y, z) is used to locate a point. To locate the point (3, 2, 4) , start at (0, 0, 0). From there move 3 units forward, 2 units right, and then 4 units up.
Example 3A: Graphing Figures in Three Dimensions
Graph a rectangular prism with length 5 units, width 3 units, height 4 units, and one vertex at (0, 0, 0).
Example 3B: Graphing Figures in Three Dimensions
Graph a cone with radius 3 units, height 5 units, and the base centered at (0, 0, 0)
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10­3 Smart Board Notes Day 1 Petre.notebook
You will graph and find
lengths of parts of
different 3D objects
Geometry Homework
10-3 p.674 #1-10, 15-23
Holt Geometry
You will graph and find
lengths of parts of
different 3D objects
Accelerated Geometry Homework
10-3 p.674 #1-10, 15-23
Holt Geometry
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