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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.