Section 3-4 Angles of a Triangle.

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Presentation transcript:

Section 3-4 Angles of a Triangle

Triangle: The figure formed by three segments joining three noncollinear points The segments are called the sides of a triangle Each of the three points is a vertex of the triangle

For Example: sides: vertices: angles: or or or C, D, E

Triangles are classified by their sides and angles. 1) By their angles: a. acute : three acute angles b. obtuse : one obtuse  c. right : one right  d. equiangular : all ’s are 

Acute Triangle Right Triangle Obtuse Triangle Equiangular Triangle

c. equilateral : all sides are  2) By their sides. a. scalene : no sides are  ; all different lengths. b. isosceles : at least 2 sides are . c. equilateral : all sides are 

Isosceles Triangle Equilateral Triangle Scalene Triangle

The sum of the measures of the angles of a triangle is 180. Theorem 3-11: The sum of the measures of the angles of a triangle is 180. 1 3 2

Remote interior angles Theorem 3-12 The measure of an exterior angle of a triangle equals the sum of the measure of the two remote interior angles Remote interior angles Exterior Angle

3 4 1 2

a statement that can be proved easily by applying a theorem Corollary: a statement that can be proved easily by applying a theorem

Corollaries: If two angles of 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.