Triangle Sum Theorem Exterior Angle Theorem Work in

Triangle Sum Theorem & Exterior Angle Theorem

Work in groups to answer the questions. Try your best. 1. 1 2 3 2. 4 5 3. Name 2 pair of alternate interior angles 5 & 3 and 4 & 1 What is the sum of m 1 + m 2 + m 3? 180° If m 4 = 65° and m 5 = 50°, what is m 2? 65° 90° 50° 130° 50° 40° 50° 90° 4. Find all the angle measures

Vocabulary • Adjacent angles – angles that share a common vertex and side • Vertical angles – a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect • Complementary angles – two angles whose sum of angle measures equals 90 degrees • Supplementary angles – two angles whose sum of angle measures equals 180 degrees • Congruent angles – angles whose angle measurements are equal

continued. . . • Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane • Exterior angles of a triangle – angles that are outside of a triangle between one side of a triangle and the extension of the adjacent side • Interior angles of a triangle – angles that are inside of a triangle, formed by two sides of the triangle • Transversal – a line that intersects two or more lines • Angle-angle criterion for triangles – if two angles in one triangle are congruent to two angles in another triangle, then the measure of the third angle in both triangles are congruent

Objectives---What we’ll learn… • Find the measurement of a missing angle by using Triangle Angle Sum Theorem. • Find the measurement of a missing angle by using Exterior Angle Theorem.

Triangle Sum Theorem The sum of the angle measures in a triangle equal 180° 1 3 2 1 + 2 + 3 = 180°

Isosceles Triangles 2 congruent sides 2 congruent base angles

Isosceles Triangles & Angle Sum Theorem Base Angles are congruent. W H E + W + H = 180 o E + 2( W) = 180 o

Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles exterior angle remote interior angles A = C + D

Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles exterior angle 2 1 3 4 = 1 + 2 4

Example 1 on Exterior Angle

Example 2 on Exterior Angle

an example with numbers find x & y 82° 30° x = 68° x y y = 112° X 60º 42º y