Math 109
Section 3.3
Isosceles Triangles
An altitude is a perpendicular line segment that connects a vertex to the opposite side
Altitude: 
Theorem 3.3.1
Corresponding altitudes of congruent triangles are congruent.
Theorem 3.3.2
The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles.
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Statement |
Reason |
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1)
|
1) Given |
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2) |
2) Definition of a bisector |
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3) |
3) Identity property |
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4) |
4) Definition of an isosceles triangle |
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5) |
5) SAS |
Theorem 3.3.3
If two sides of a triangle are congruent, then the angles opposite these sides are also congruent
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Statement |
Reason |
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1) |
1) Given |
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2) Construct bisector of |
2) All angles have a bisector |
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3) |
3) Theorem 3.3.2 |
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4) |
4) CPCTC |
Theorem 3.3.4
If two angles of a triangle are congruent, then the sides opposite these angles are also congruent.
|
Statement |
Reason |
|
1) |
1) Given |
|
2) Construct a perpendicular |
2) There is exactly one perpendicular segment to a point on a given line. |
|
3) |
3) Identity Property |
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4) |
4) Definition of perpendicular lines |
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5) |
5) All right angles are congruent |
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6) |
6) AAS |
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7) |
7) CPCTC |
segment to 
Corollary 3.3.5
An equilateral triangle is also equiangular
Corollary 3.3.6
An equiangular triangle is also equilateral
Exercises
Page 135-136
2) If 
, then which angles are congruent
4)
6) Givenand 
, find 
The term determined is used to describe a unique solution.
The term undetermined is used to describe a situation with an infinite solutions.
The term over determined is used to describe to describe a situation where there is no solution.
Use the figure answer questions 9-14
10) Draw a segment with endpoints A and B
Determined
12) Draw segment 
perpendicular to line m.
Overdetermined
26) Find x if the perimeter of 
is 68, AB = x, BC = 1.4x
