Find the value of x. 1. x + 2x + 3x = 180 6x = x + x + 40 = x + (x + 1) + 35 = x + 40 = 180 x = 70 3x + 36 = x = 48 x = x = x = Date: Topic: Triangles & Triangle Angle Sum Theorem (6.5)

A Triangle is the figure formed by the segments that join three noncollinear points. Each segment is called a side of the triangle. Each point is called a vertex. The angles determined by the sides are called the interior angles of the triangle. P Q triangle PQR Often a triangle can be classified by its sides. R 1 23 Equilateral 3 equal sides Isosceles 2 equal sides Scalene no equal sides

Triangle A three-sided polygon. The sum of the angles of a triangle is 180 degrees. Equilateral Triangle or Equiangular Triangle A triangle having all three sides of equal length. The angles of an equilateral triangle all measure 60 degrees. Examples:

Isosceles Triangle A triangle having two sides of equal length. Examples:

Scalene Triangle A triangle having three sides of different lengths. Examples:

A triangle can be classified by its angles. Acute Triangle A triangle having three acute angles. Examples:

Obtuse Triangle A triangle having an obtuse angle. One of the angles of the triangle measures more than 90 degrees. Examples :

Right Triangle A triangle having a right angle. One of the angles of the triangle measures 90 degrees. The side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called the legs.

Acute 3 acute angles Right 1 right angle Equiangular 3 equal angles Obtuse 1 obtuse angle Triangle Sum Theorem: The sum of the measure of the angles of a triangle is 180˚. Find the measure of b. A triangle can be classified by its angles. b 36  b = 180 b = b = 56˚

Find the measures of each angle. 27˚ 2g g+9 2g + (g + 9) + 27 = 180 3g + 36 = g = 48 3g = = 2(48) = 96˚ = = 57˚