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Notes Sec 4.1.notebook Unit 4: Classifying Triangles (4.1) p.194201 Triangle: a figure formed by 3 segments that join 3 noncollinear points A triangle can be named using its sides or its angles Recall some definitions: Vertex: points where the angles are formed in the triangle Adjacent sides: 2 sides sharing a common vertex opposite side of < A C adjacent sides A B 1 Notes Sec 4.1.notebook Hypotenuse:the opposite side of the right angle Legs:the sides that form the right angle of a right triangle the congruent sides of an isosceles triangle leg hypotenuse leg leg leg base Exterior Angles In an isosceles triangle, we refer to the base and the legs. base angles are also congruent Interior Anlges 2 Notes Sec 4.1.notebook Names of Triangles Classified by Sides: Equilateral: 3 sides congruent Equilateral triangles also equiangular (equal angles)! Isosceles: At least 2 sides congruent Scalene: No Sides Congruent Base angles of an isosceles triangle are congruent! Classified by Angles: Acute: 3 acute angles Equiangular: 3 congruent angles (also acute and 3 sides are congruent) Right: 1 right angle Obtuse: 1 obtuse angle 3 Notes Sec 4.1.notebook Warmup Problems: True or False (#14) 1. It is possible to draw an acute scalene triangle. 2. It is possible to draw an obtuse equilateral triangle. 3. It is possible to draw a right isosceles triangle. 4. It is possible to draw a right scalene triangle. 5. Classify the triangle with the most specific name possible: 46O 46O 88O Sec. 4.1 (continued) Triangle Sum Theorem: the sum of the measures of the interior angles of a triangle is 180 degrees. m<A + m<B + m<C = 180 o B A C 4 Notes Sec 4.1.notebook 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. m<1 = m<A + m< B A 1 B Exterior Angles Facts: 0 1. the sum of the exterior angles of a triangle is 360 2. an exterior angle is equal to the sum of its 2 remote interior angles (the nonadjacent angles) Exterior Angles Interior Anlges An exterior angle forms a linear pair with its adjacent interior angle, so they sum to what? 5 Notes Sec 4.1.notebook Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary. m<A + m<B = 90 o A B Solve for x. 2. 1. 2x0 3x0 (4x + 8)0 (2x 15)0 6 Notes Sec 4.1.notebook 3. 4. Classify the triangle by sides and angles. 360 50 23 19 770 5. 110 x0 20 16 6. An equilateral triangle has 1 angle measure of 4x0. What is the value of x? 7 Notes Sec 4.1.notebook 7. 8. (5x + 4)0 (4x 8)0 420 8 Notes Sec 4.1.notebook 9