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Two- and Three-Dimensional Figures

Two- and Three-Dimensional Figures. Advanced Geometry Inductive Reasoning Lesson 3. Polygon. Examples. NO HOLES. NO CURVES. SIDES CANNOT OVERLAP. Named by: all vertices written in consecutive order. Concave. “caves in”. extend the sides. extend the sides. Convex.

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Two- and Three-Dimensional Figures

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  1. Two- and Three-Dimensional Figures Advanced Geometry Inductive Reasoning Lesson 3

  2. Polygon Examples NO HOLES NO CURVES SIDES CANNOT OVERLAP Named by: all vertices written in consecutive order

  3. Concave “caves in” • extend the sides • extend the sides Convex • all extensions lie outside the figure • any extension crosses inside the figure

  4. Names of Polygons triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon n - gon

  5. Regular Polygon convex polygon all the sides are congruent and all angles are congruent

  6. Examples: Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Pentagon convex regular

  7. Perimeter – the sum of the lengths of the sides of a polygon Area – the number of square units needed to cover a surface Perimeter and Area of a Rectangle ADD ALL SIDES

  8. Circumference and Area of a Circle Circumference – the distance around a circle Area

  9. Example: Mr. Smith has a circular fence that encloses an area with a diameter of 12 feet. Using the same fence, he wants to create a square fence. What is the maximum side length of the square?

  10. Example: Find the perimeter of a square with an area of 30 square centimeters.

  11. Example: Find the circumference of a circle with an area of 36 square units.

  12. Example: Find the length of each side of the polygon below if its perimeter is 20 units.

  13. Polyhedron Definition: a solid with all flat surfaces that enclose a single region of space • All flat surfaces are • called faces. • The line segments where • the faces intersect • are edges. • The points where the • edges intersect are • vertices.

  14. Prisms The two bases are parallel AND congruent. Named by: the shape of the bases Triangular Prism Rectangular Prism Pentagonal Prism A regular prism has bases that are regular polygons.

  15. Pyramids one base Named for: the base Triangular Pyramid Rectangular Pyramid Hexagonal Pyramid

  16. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 62 in your textbook.

  17. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 61 in your textbook.

  18. Cylinders Cones Spheres one circular base The two bases are congruent, parallel circles. NOT polyhedra (polyhedrons)

  19. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 62 in your textbook.

  20. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 61 in your textbook.

  21. Height vs. Slant Height

  22. Surface Area and Volume Prisms Pyramids

  23. Surface Area and Volume Cylinders Cones

  24. Examples: Find the surface area and volume of the square prism.

  25. Examples: Find the surface area and volume of the square pyramid. This picture is on page 62 in your textbook.

  26. Examples: Find the surface area and volume of the square pyramid.

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