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Objective: 4.1 Classifying Triangles 4.2 – Angles in Triangles Warm Up - State the number of sides in each geometric figure. 1. Trapezoid 2. Equilateral triangle 3. Rhombus 4. Parallelogram 5. Scalene triangle Objective: 4.1 Triangles and Angles Triangles • Triangle-figure formed by 3 segments joining 3 noncollinear pts. • Triangles are named by these three pts (ΔQRS) Q R S By Angle Measures Triangle Classification Acute Triangle Three acute angles By Angle Measures Triangle Classification Equiangular Triangle Three congruent acute angles **This is a special case of “acute triangle” By Angle Measures Triangle Classification Right Triangle One right angle By Angle Measures Triangle Classification Obtuse Triangle One obtuse angle By Side Lengths Triangle Classification Equilateral Triangle Three congruent sides By Side Lengths Triangle Classification Isosceles Triangle At least two congruent sides By Side Lengths Triangle Classification Scalene Triangle No congruent sides • Each of the three pts are vertices • Adjacent sides2 sides sharing a common vertex • Third side is opposite the given vertex. B A C Parts of a Right Triangle Leg Leg Parts of an Isosceles Triangle Leg __ ___ Base Leg Ex. 1 It is possible to draw a right isosceles triangle? Is it possible to draw an isosceles equilateral triangle? Is it possible to draw an obtuse scalene triangle? Interior Angles A ))) B C Exterior Angles (formed by extending the sides) ( E D F Thm 4.1 - Triangle Angle Sum Theorem • The sum of the measures of the interior angles of a triangle is 180o. A • mA + mB+ mC=180o B C Thm 4.2 - Exterior Angles Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. • m1 = mA+ mB B Remote Interior Angles A 1 C Ex: Find the value for x • Use the Exterior Angle Thm A 65 B x (2x + 10) C Third Angles Theorem D A E F B C If two angles of ABC are congruent two angles of DEF, then the third angles must be congruent Corollaries to Triangle Sum Thm (Corollary- a statement easily A proved using a thm.) • The acute angles of a right triangle are complementary. • There can be at most one right or obtuse angle in a triangle. B A is comp. to C B is the only right angle C Ex 3: Find the measure of each acute angle. * Use the corollary to the triangle sum thm • Let x = m < A and m < B = 2x B 2x x C A