**Geometry Chapter 4.1 Triangles and Angles**

**I) Vocabulary**:

**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.

**H) Theorem**:

**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