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Section 2.3 -
Angle Properties in Triangles
Triangle Sum Theorem
The sum of the three interior angles of a triangle is 180 o
Isosceles Triangle Theorem
In any isosceles triangle, the angles opposite the equal sides are equal.
Exterior Angle of a triangle –
Determine the measure of angles 1 through 4. Justify each measurement.
Determine the measure of angles "a" through "c". Justify each measurement.
Using a two-column proof, prove that a + b = f + g if c = e.
Using a two-column proof, prove the measure of an exterior angle (a) of a triangle is equal to the
sum of the measures of the two non-adjacent interior angles (b and c).
Your turn:
Example #1:
Find the missing angles:
a)
Example #2:
Can you prove that e = a + b ?
b)
Example #3: Find the missing angles.
Example #4: Is FG HI, how do you know?
Section 2.4
Angle Proportions in Polygons
Polygon –
Regular polygon –
Convex polygon –
Non-convex (concave) polygon –
Polygon
Interior Angles-
Exterior Angles –
Number of sides
Number of triangles
Sum of Angle
measures
Ex(1)
Determine the sum of the measures of the interior angles of a polygon with 25 sides.
Ex(2) Determine the measure of each interior angle of a regular polygon with 30 sides.
Ex(3)
The sum of the measures of the interior angles of an unknown polygon is 900o. What type of
polygon is it?
Ex(4)
Determine the measure of each exterior angle of a regular dodecagon (12 - sided).
Ex(5)
Determine the value of x in the diagram below, then find the measure of each angle indicated.
Ex(6) Find the measures of angles A, B, C, D, and E.