Geometry Chapter 4.1 Triangles and Angles
A) Triangle - is a figure formed by three segments joining three noncollinear points.
B) Classification of triangles:
1) By sides:
a) Equilateral Triangle - has 3 congruent sides
b) Isosceles Triangle - has at least 2 congruent sides
c) Scalene Triangle - has no congruent sides
2) By angles:
a) Acute Triangle - has 3 acute angles
b) Equiangular Triangle - has 3 congruent angles that measure 60 degrees each
c) Right Triangle - has one right angle and 2 acute angles
d) Obtuse Triangle - has one obtuse angle and 2 acute angles
C) Vertex - each of the three points joining the sides of a triangle (plural - vertices)
D) Adjacent Sides - in a triangle, two sides sharing a common vertex.
E) Right triangles have 2 sides that form the right angle called the legs. The side opposite the right angle is the hypotenuse of the triangle.
F) Interior angles - when the sides of a triangle are extended, other angles are formed. the three original angles are the interior angles.
G) Exterior angles - the angles that are adjacent to the interior angles.
1) Triangle sum theorem - the sum of the measures of the interior angles of a triangle is 180 degrees.
2) Exterior Angle Theorem - the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
I) Corollary to a theorem - is a statement that can be proved easily using the theorem.
Example: The acute angles of a right triangle are complementary.
Example: given Triangle ABC with side BC extended through point D, if angle A = 65 degrees and angle ACD = 2x + 10 and angle B = x, solve for x.
angle A + angle B = angle ACD
65 + x = 2x + 10
55 = x