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Geometry 2
Euclidean Geometry in the Plane
Given parallel lines r and s, what do we know to be true
about the measures of the following sets of angles?
1 and 2
1 and 4
3 and 6
2 and 7
4 and 8
Assume m2 is not equal to m7.
Then m2 > m7
m2 + m4 = 180 degrees
m7 = m6
m4 + m6 < m4 + m2 = 180 degrees so the lines are not
parallel.
If m1 = m2, then lines r and s are parallel.
Assume r and s are not parallel, then you can show that a
set of interior angles are less than 180 degrees and m1 and
m2 cannot be equal.
Triangles
Why do we study triangles so diligently?
Classified by length of side:
Scalene: Sides are unequal.
Isosceles: Two sides are equal.
Equilateral: Three sides are equal.
Classified by length of angle:
Right: One 90 degree angle.
Obtuse: One angle greater than 90 degrees.
Acute: All angles less than 90 degrees.
The classifications are interrelated.
Isosceles triangles have what characteristics of angles?
Equilateral triangles have what characteristics of angles?
m1 = m2 and m3 = m4 = m5.
Given triangle, ABC is isosceles with AB  BC and
AD  CE and F is the midpoint of AC , prove ADC  CEF .
is equilateral with m1 = m2 = m3, show that
FBA  ECB  DAC .
ABC
Hexagon: What do you know about this figure?
Six sides and six angles and made up of triangles.
Polygon:
Triangles are the building blocks.
Triangles are rigid: Measurement of three sides determine
the triangle. Why?
What are examples of polygons with number of sides
greater than 3 where the sides determine the polygon?
Definition: Regular polygons have equal sides and equal
angles.
Perimeter: Distance around a figure.
Area: Number of square units contained in a closed plane
figure.
Parallelogram: Area = Base x Height
Triangle: area = bh/2
Trapazoid: area = h(a+b)/2
Circles
What is  ?
The ratio of the circumfrance of a circle to its diameter?
c   d  2 r
area   r 2