4.1 Triangles and Angles October 6, 2011

Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: Classify triangles by their sides and angles. Find angle measures in triangles DEFINITION: A triangle is a figure formed by three segments joining three non-collinear points.

Names of triangles Triangles can be classified by the sides or by the angle An Equilateral triangle has 3 congruent sides An Isosceles Triangle has 2 congruent sides A Scalene triangle has no congruent sides

Acute Triangle M∠A = 42° M∠B = 70° M∠C = 68° 3 acute angles A B C

Equiangular triangle 3 congruent angles. An equiangular triangle is also acute.

Right Triangle Obtuse Triangle 1 right angle One obtuse angle

Parts of a triangle Each of the three points joining the sides of a triangle is a vertex.(plural: vertices). A, B and C are vertices. Two sides sharing a common vertex are adjacent sides. The third is the side opposite an angle adjacent Side opposite A adjacent CA and BA are adjacent sides because they share vertex A. CB is the side opposite of vertex A.

Right Triangle The side of the triangle opposite of the right angle is the hypotenuse of a right triangle. The sides that form the right angle are the legs. hypotenuse leg leg

Isosceles Triangles An isosceles triangle has only two congruent sides. These two sides are the legs of the isosceles triangle. The third is the base. A leg base B leg C

Using Angle Measures of Triangles Smiley faces are interior angles and hearts represent the exterior angles

Ex. 3 Finding an Angle Measure. Exterior Angle Theorem: The measure of an exterior angle is the sum of the 2 NON-ADJACENT interior angles. m1 = m A +m B x + 65 = (2x + 10) 65 = x +10 55 = x 65 A (2x+10) x 1 B

Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. m∠A + m∠B + m∠C = 180°. A 40° B 60° 80° C