Triangle Sum Theorem & Exterior Angle Theorem
Work in groups to answer the questions. Try your best. 1 3 2 4 5 Name 2 pair of alternate interior angles 5 & 3 and 4 & 1 2. What is the sum of m1 + m2 + m3? 180° If m4 = 65° and m5 = 50°, what is m2? 65° 90° 40° 130° 50° 50° 4. Find all the angle measures 40°
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° 3 2 1 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 = 180o E + 2(W) = 180o
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 remote interior angles 3 2 1 4 4 = 1 + 2
Example 1 on Exterior Angle
Example 2 on Exterior Angle
an example with numbers find x & y 82° x = 68° y = 112° 30° x y 60º 42º y X