1. Introduction to Triangles

2. Can be classified by the angle measures
Triangles
Can be classified by the angle measures

3. Has three acute angles (less than 90 degrees)
Acute Triangle
Has three acute angles (less than 90 degrees)

4. Triangle with one obtuse angle (greater than 90 degrees)
Obtuse Triangle
Triangle with one obtuse angle (greater than 90 degrees)

5. Has one right angle (90 degree)
Right Triangle
Has one right angle (90 degree)

6. Can be classified by the number of congruent sides
Triangles
Can be classified by the number of congruent sides

7. Has no congruent sides (all angles, and sides are different sizes)
Scalene Triangle
Has no congruent sides (all angles, and sides are different sizes)

8. Has at least two congruent sides
Isosceles Triangle
Has at least two congruent sides
least

9. the angles opposite the congruent sides are also congruent
Isosceles Triangle
the angles opposite the congruent sides are also congruent

10. Equilateral Triangle All three sides are congruent
Congruent – same size and shape

11. Which can only happen in a equilateral triangle
Equiangular Triangle
Triangle with 3 congruent angles
Which can only happen in a equilateral triangle

12. Classifying Triangles

13. Triangles Cut any shape triangle out of a sheet of paper .
Tear off the corners. Piece them together by having the corners touch.
The corners form what type of angle?

14. The sum of the angles of a triangle is 180 degrees
Triangles
The sum of the angles of a triangle is 180 degrees

15. Proving sum of the angles of a triangle is 180 degrees
Prove A+B + C = 180 G C H 1 2 3
1. Create a line GH that is parallel to AB
2. Label the angles along the straight line, 1, 2, 3 1 3 A B
3. Use what you know about alternate interior angles and label the lower angles in the triangle
4. Since angles 1,2, & 3 create a straight line, we know their sum is 180°.
5. Therefore, we know that that the sum of the internal angles of a triangle always add to 180°

16. If all the angles must add to 180 and be the same…..
Equiangular Triangle
Triangle with 3 equal angles
If all the angles must add to 180 and be the same…..
Then,
x+x+x = 180
3x = 180
X = 60

17. If you know 2 angles, then you can always figure out the 3rd
Triangles
If you know 2 angles, then you can always figure out the 3rd

18. Triangle Inequalities

19. Triangle Inequality Theorem:
The sum of two sides of a triangle must be greater than the length of the third side.
a + b > c
a + c > b
b + c > a
Example:
Determine if it is possible to draw a triangle with side measures 12, 11, and 17.
> 17  Yes
> 12  Yes
> 11  Yes
Therefore a triangle can be drawn.

20. Angle Side Relationship
The longest side is across from the largest angle.
The shortest side is across from the smallest angle. 54 37 89 B C A
BC = 3.2 cm
AB = 4.3 cm
AC = 5.3 cm

21. Triangle Inequality – examples…
For the triangle, list the angles in order from least to greatest measure. C A B
4 cm
6 cm
5 cm

22. Exterior Angles B x y w A C
An exterior angle formed by a side of the triangle and the extension of another side . In this case, w
The remote interior angles the two nonadjacent interior angles. In this case x & y

23. Find the measure of angle B
The sum of the measure of the angles of a triangle is 1800.
Lets call the 3rd internal angle z
400
800
600 z
1200  A C D
z = 180
120 + z = 180
z = 60
ACB and BCD are supplementary
60 + x = 180
 = 120