4-1 triangles and angles. theorem 4.1: triangle sum the sum of the measures of the interior angles...

4-1 Triangles and Angles4-1 Triangles and Angles

Theorem 4.1: Triangle Sum

The sum of the measures of the The sum of the measures of the interior angles of a triangle is 180interior angles of a triangle is 180 ..

x

y

z

x + y + z = 180

Theorem 4.2: Exterior AngleTheorem 4.2: Exterior Angle

The measure of an exterior angle of a The measure of an exterior angle of a triangle is equal to the sum of the triangle is equal to the sum of the measures of the two nonadjacent measures of the two nonadjacent (remote) interior angles.(remote) interior angles.

41

2

3

mm4 = m4 = m1 + 1 + mm2 2

Triangle Sum CorollaryTriangle Sum Corollary

The acute angle of a right triangle are The acute angle of a right triangle are complementary.complementary.

a

b

a + b = 90

Classifying Triangles by SidesClassifying Triangles by Sides

Equilateral TriangleEquilateral TriangleAll sides are congruent.All sides are congruent.

Isosceles TriangleIsosceles TriangleAt least two sides are congruent.At least two sides are congruent.

Scalene TriangleScalene TriangleNo sides are congruent.No sides are congruent.

Classifying Triangles by AnglesClassifying Triangles by Angles

Equiangular TriangleEquiangular TriangleAll angles are congruent.All angles are congruent.

Right TriangleRight TriangleOne angle is a right angle.One angle is a right angle.

Obtuse TriangleObtuse TriangleOne angle is an obtuse angle.One angle is an obtuse angle.

Acute TriangleAcute TriangleAll angles are acute angles.All angles are acute angles.

Right TrianglesRight Triangles

CA

B

hypotenuse

leg

leg

Isosceles TrianglesIsosceles Triangles

base

legleg

Find the measure of the exterior angle.