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

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

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

4. Names of Polygons triangle quadrilateral pentagon hexagon heptagon
# of sides and angles
Name of Polygon 3 4 5 6 7 8 9 10 n
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
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 and Area of a Rectangle
Area – the number of square units needed to cover a surface
Perimeter – the sum of the lengths of the sides of a polygon
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
Hexagonal
Pyramid

16. This picture is on page 62 in your textbook.
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. This picture is on page 61 in your textbook.
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. NOT polyhedra (polyhedrons)
Cylinders
Cones
Spheres
The two bases are congruent, parallel circles.
one circular base
NOT polyhedra (polyhedrons)

19. This picture is on page 62 in your textbook.
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. This picture is on page 61 in your textbook.
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. This picture is on page 62 in your textbook.
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.