1. Sec 5.4: Classifying Triangles
Objectives:
• Classify triangles by their sides
• Classify triangles by their angles
• Triangle Sum Postulate

2. Concept: Classifying Triangles
2 Ways to Classify Triangles:
By the number of congruent sides
By the types of angles in the triangle

3. Classify by Sides

4. Concept: Equilateral Triangles
Equilateral: Equi –– lateral
equal
sides
Any triangle where all 3 sides are equal.
Note: If all 3 sides are equal, then all
3 angles are also equal.

5. Concept: Equilateral Triangles
The “tick” marks indicate that the segments are congruent.

6. Concept: Isosceles Triangle
Isosceles: Any triangle with at least two congruent sides.
Note: if 2 sides are congruent,
then 2 angles are congruent.

7. Concept: Scalene Triangle
Scalene: NO sides are the same length.
Note:
Each side
has a different
number of “tick” marks.
This means each side is a
Different length. Each angle is
marked with a different number
of arcs. This means that all angles are
different.

8. Concept: Classifying Angles
Zero angle: x = 0º
Acute angle: 0º < x < 90º
Right angle: x = 90º
Obtuse angle: 90º < x < 180º
Straight angle: 0º < xº < 90º
By the types of angles in the triangle

9. Classify by Angles

10. Concept: Obtuse Triangle
Obtuse: Any triangle with exactly one obtuse angle.
Note: It is not possible to have more
than one obtuse angle in a
triangle.

11. Concept: Acute Triangle
Acute: Any triangle where all three angles are acute.

12. Concept: Right Triangle
Right: Any triangle that has exactly one right angle.

13. Concept: Triangle Sum Rule
The sum of the interior angles of ANY triangle is 180º.

14. Concept: Application

15. Concept: Application x = 15 3x + 5x + 5 + 4x – 5 = 180º
1. Set up equation 3x
+ 5x + 5
+ 4x – 5
= 180º
3x + 5x x – 5 = 180º
2. Combine Like Terms
12x
+ 0
= 180º
12x = 180º
x = 15
3. Divide by 12 12 12

16. Concept: Application x = 15 A =3x A = 4x – 5 A = 5x + 5 A = 3(15)

17. Woot! Woot! Concept: Application x = 15 Check:
45º º º = 180º ?
Woot! Woot!
125º+ 55º = 180º ?
180º = 180º ?