1. Applying Triangle Sum Properties
Lesson 4-1

2. Triangles
Triangles are polygons with three sides.

3. Scalene Triangles Scalene triangles do not have any congruent sides.
In other words, no side has the same length.
6cm
3cm
8cm

4. Isosceles Triangle A triangle with 2 congruent sides.
2 sides of the triangle will have the same length.

5. Equilateral Triangles
All sides have the same length

6. Acute Triangle
A triangle where all angles are acute angles.

7. Right Triangle
A triangle with one right angle.

8. Obtuse Triangle
A triangle with one obtuse angle.

9. Equiangular Triangles
All angles have the same angle measure.

10. Classify by its SIDES

11. Classify by its ANGLES

12. Classify by its angles AND its sides

13. Obtuse Isosceles Right Scalene Acute Obtuse Right Equilateral
Sketch an example of the type of triangle described. Mark the triangle to indicate what information is known. If no triangle can be drawn, write “not possible”
Obtuse Isosceles
Right Scalene
Acute Obtuse
Right Equilateral

14. Worksheet #1

15. Interior Angles vs. Exterior Angles
Interior Angle: When the sides of a triangles are extended, the three original angles. Exterior Angles: When the sides of a triangles are extended, the angles that are adjacent to the interior angles.

16. Interior or Exterior?

17. Interior or Exterior?

18. Interior or Exterior?

19. Triangle Sum Theorem (Postulate Sheet)
States that the sum of the interior angles is 180.
102°
56°
22°

20. Example Find the measure of each indicated angle. 98° 20° ? 54° 32°
53°

21. The sum of the angles is 180, so
Example
Find the value of x
The sum of the angles is 180, so
x + 3x + 56= 180
4x + 56= 180
4x = 124
x = 31

22. Example
Find the measure of angle A
84°
x +58°
x + 52

23. Find the Value for X 2x + 15 3x 2x + 15 + 3x + 90 = 180 5x + 105 = 180

24. Corollary to the Triangle Sum Theorem (Postulate Sheet)
Acute angles of a right triangle are complementary.
3x + 10
5x +16

25. Worksheet #2 (front)

26. Exterior Angle Sum Theorem
The measure of the exterior angle of a triangle is equal to the sum of the non-adjacent interior angles of the triangle

27. = y
158 = y

28. 2x + 40 = x + 72
2x = x + 32
x = 32

29. Find x and y
3x + 13
46o
8x - 1
2yo

30. Worksheet #2 (Back)