1. Triangle Sum Theorem & Exterior Angle Theorem

2. Work in groups to answer the questions. Try your best.1 3 2 4 5
Name 2 pair of alternate interior angles
5 &  and 4 & 1
2. 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°
40°
130°
50°
50°
4. Find all the angle measures
40°

3. 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

4. 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

5. 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.

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

7. Isosceles Triangles
2 congruent sides
2 congruent base angles

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

9. 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

10. 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

11. Example 1 on Exterior Angle

12. Example 2 on Exterior Angle

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