GEOMETRY CLASSIFYING TRIANGLES Goal to classify triangles by

GEOMETRY - CLASSIFYING TRIANGLES Goal, to classify triangles by their sides and by their angles.

GEOMETRY - CLASSIFYING TRIANGLES Classification of triangles by SIDES Equilateral triangle, Isosceles triangle, Scalene triangle, 3 congruent sides. at least 2 congruent sides no congruent sides.

GEOMETRY - CLASSIFYING TRIANGLES Classification of triangles by ANGLES Equiangular Triangle; 3 congruent angles Right triangle; 1 right angle Acute Triangle; 3 acute angles Obtuse triangle; 1 obtuse angle

GEOMETRY - CLASSIFYING TRIANGLES

- INTERIOR & EXTERIOR ANGLES GEOMETRY B 1 A 2 interior The three angles of a triangle are called the angles INTERIOR ANGLES C 3 When the sides of a triangle are extended, other angles are formed. The angles that are adjacent to the interior angles are the exterior angles.

- TRIANGLE SUM THEOREM GEOMETRY The sum of the measures of the angles of a triangle is 180°. m + m = 180° B C A

- TRIANGLE SUM THEOREM GEOMETRY Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. m A + m B = 90°. C A B

- TRIANGLES GEOMETRY Exterior Angle The exterior angle and the adjacent interior angle are supplementary. B Exterior angle A 60 C 1120

- TRIANGLES GEOMETRY Exterior Angle Theorem + B A 30 = 100 50 C 130

- TRIANGLES GEOMETRY 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 (remote interior angles). m A + m B = m 1 B A C 1

- TRIANGLES GEOMETRY Triangle Sum Theorem (1) 46 55 79 ?

GEOMETRY - TRIANGLES (2) 3 x (x+5)+3 x+15 = 180 4 x+20 = 180 x+5 15 4 x = 160 x = 40

- TRIANGLES GEOMETRY (3) 92 ? 161 19 73

GEOMETRY - TRIANGLES (4) 35 25 63 116 x? 91 y? 119