Download Definition: A triangle is figure formed by three segments joining three

math424j8.notebook
January 08, 2015
Definition:
A triangle is figure formed by three segments joining three noncollinear points. Each of the three points is a vertex of the triangle. The segments are the sides of the triangle.
Classification of Triangles by the number of congruent sides:
Scalene Triangle:
No sides are congruent.
Isosceles Triangle:
At least two sides are congruent.
Equilateral Triangle:
All three sides are congruent.
Classification of triangles by their angles:
Acute Triangle:
Three acute angles.
Obtuse Triangle:
Contains one obtuse angle.
Right Triangle:
Contains one right angle
Equiangular Triangle:
All angles are congruent.
math424j8.notebook
January 08, 2015
Theorem: The sum of the measures of the angles of a triangle is 180.
1
3
2
math424j8.notebook
January 08, 2015
A statement that can be proved easily by applying a theorem is often called a corollary of the theorem.
If two angles in one triangle are congruent to two angles of another triangle, then the third angles are congruent.
Each angle of an equiangular triangle has measure 60.
In a triangle, there can be at most one right angle or obtuse angle.
The acute angles of a right triangle are complementary.
math424j8.notebook
January 08, 2015
hw Jurgenson: p. 98­99 # 23,25,29,31, Bumby p. 156 Challenge 1,2
Exterior angle theorem
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
A
1
Proof:
2
B
3
4
C
D
math424j8.notebook
January 08, 2015
math424j8.notebook
January 08, 2015
Identify exterior angles in the diagram below, use the exterior angle theorem to show the relationship between the angle
and its remote interior angles.
8
C
7
6
B
math424j8.notebook
January 08, 2015
math424j8.notebook
January 08, 2015
math424j8.notebook
January 08, 2015