Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Noether's theorem wikipedia , lookup
Golden ratio wikipedia , lookup
Multilateration wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
Lesson 4.1 Classifying Triangles Today, you will learn to… * classify triangles by their sides and angles * find measures in triangles Equilateral Triangle 3 congruent sides Isosceles Triangle 2 congruent sides Scalene Triangle no congruent sides Equiangular Triangle 3 congruent angles Acute Triangle 70° 60° 50° 3 acute angles Obtuse Triangle 95° 60° 25° 1 obtuse angle Right Triangle 30° 60° 1 right angle We classify triangles by their sides and angles. SIDES Equilateral Isosceles Scalene ANGLES Equiangular Acute Obtuse Right Identify the side opposite the given angle. A C B CB is opposite _____ A. AC is opposite _____ B. AB is opposite _____ C. Leg? leg hypotenuse ? leg Leg? leg ? base leg Theorem 4.1 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is ________ 180° 1. Find m X. Y mX = 44˚ 61º Z 75º X If the sum of the interior angles is 180º, what do you know about 1 and 2? 1 2 Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary _________________. 2. Find m F. D 54˚ + mF = 90˚ 54˚ E mF = 36˚ F 3. Find m 1 and m 2. 50º 70º m1 = 60˚ m2 = 120˚ exterior angle 1 2 adjacent angles Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. 1 2 m1 + m2 = m4 3 4 m1 + m2 + m3 = 180˚ m4 + m3 = 180˚ m1 + m2 = m4 1 2 Sum of nonadjacent interior s 3 4 = ext. 4. Find mE. E m E + 60˚ = 110˚ m E = 50˚ 60˚ D 110˚ F G 5. Find x. E x˚ 60˚ D x + 60 = 3x + 10 x = 25 (3x + 10)˚ F G