4-1 Triangles and Angles. Theorem 4.1: Triangle Sum The sum of the measures of the interior angles of a triangle is 180 . xx yy zz  x +

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Presentation transcript:

4-1 Triangles and Angles

Theorem 4.1: Triangle Sum The sum of the measures of the interior angles of a triangle is 180 . xx yy zz  x + y + z = 180 

Theorem 4.2: Exterior Angle The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent (remote) interior angles m  4 = m  1 + m  2

Triangle Sum Corollary The acute angle of a right triangle are complementary. aa bb  a + b = 90 

Classifying Triangles by Sides Equilateral Triangle All sides are congruent. Isosceles Triangle At least two sides are congruent. Scalene Triangle No sides are congruent.

Classifying Triangles by Angles Equiangular Triangle All angles are congruent. Right Triangle One angle is a right angle. Obtuse Triangle One angle is an obtuse angle. Acute Triangle All angles are acute angles.

Right Triangles C A B hypotenuse leg

Isosceles Triangles base leg

Find the measure of the exterior angle.