The beginnings of the homework due Friday'

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• 8.2
• The beginnings of the homework due Friday.
• Section 8.2
• 8ad(theres some paper in the back of your
  Explorations book), 16d, 18ab, 29

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1. Curves

• What are some differences between all the shapes

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First of all, theyre all called curves.

• It sounds a little weird. Mathematically, a
  straight lines it actually a straight curve.

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Simple Curves

• A figure is a simple curve in the plane if we can
  trace the figure in such a way that we never
  touch a point more than once,
• An example of a not simple curve

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Closed Curve

• A figure is a closed curve if we can trace the
  figure in such a way that our starting point and
  our ending point are the same.

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Simple Closed Curve
Interior

• A simple closed curve is the plane is a curve
  that we can trace without going over any point
  more than once while beginning and ending at the
  same point.

Exterior
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2. Polygons

• Simple closed curves in the plane composed only
  of line segments.
• The line segments that make up the polygon are
  called sides.
• The point at which any two sides meet is called a
  vertex, the plural of which is vertices.
• Polygonmany sides

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• Number of sides Name
• 3 sides Triangle
• 4 sides Quadrilateral
• 5 sides Pentagon
• 6 sides Hexagon
• 7 sides Heptagon
• 8 sides Octagon
• n sides n-gon

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3. Triangles

• Look at the group of triangles in groups (max of
  3). Separate them into two or more groups so that
  members of each group share a characteristic in
  common. Can you come up with a name for each
  subset? Do this in as many ways as possible.

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What did you come up with?
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Looking at sides
Equilateral Triangle -All three sides have the
same length. Do we remember anything else about
Equilateral Triangles?
Any time we position a triangle so that one side
is horizontal, we call that side the base.
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Isosceles Triangle -At least two sides have the
same length. Do we remember anything else about
Isosceles Triangles?
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Scalene Triangle -If all three sides have
different lengths-that is, no two sides have the
same length
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Look at angles
Right Triangle -A triangle that has one right
angle.
Obtuse Triangle -A triangle that has one obtuse
angle.
Acute Triangle -A triangle that has three acute
angle.
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• Can you have a triangle with a right and a obtuse
  angle?

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Can you tell me about the other kinds of angles
for the triangles?

• 1st angle 2nd angle 3rd angle Name of Triangle
• Right Right Triangle
• Obtuse Obtuse Triangle
• Acute Acute Triangle

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Consider angles and sides

• Equilateral Acute
• Isosceles Right
• Scalene Obtuse
• What combinations are possible?
• Impossible?

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4. Venn Diagrams

• Skipped the section, but its useful. Does anyone
  remember how they work?
• Examples

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• Try to come up with some Venn Diagrams for types
  of triangles. Put them up around the classroom.

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5. Special Line Segments

• A median is a line segment that connects a vertex
  to the midpoint of the opposite side.

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• An angle bisector is a line segment that bisects
  an angle of a triangle.

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• A perpendicular bisector is a line that goes
  through the midpoint of a side and is
  perpendicular to that side.

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• An altitude is a perpendicular line segment that
  connects a vertex to the side opposite that
  vertex.