1. Lesson 4 – 1 Classifying Triangles
Geometry
Lesson 4 – 1
Classifying Triangles
Objective:
Identify and classify triangles by angle measures.
Identify and classify triangles by side measures.

2. Classifications of Triangles by Angles
Acute Triangle
3 acute angles
Obtuse Triangle
1 obtuse angle
Right Triangle
1 right angle
Equiangular Triangle
3 congruent acute angles

3. Classify each triangle as acute, equiangular, obtuse, or right.

4. Example
Classify triangle PQR as acute, equiangular, obtuse, or right. Explain your reasoning.
104
Triangle PQR is obtuse since it has 1 obtuse angle
Of 104 degrees.

5. Your Turn
Use the diagram to classify triangle PQS as acute, equiangular, obtuse, or right. 90
Triangle PQS is a right triangle since it has a right
angle.

6. Classifying Triangles by Sides
Isosceles Triangle
at least 2 congruent sides
Equilateral Triangle
3 congruent sides
Scalene Triangle
No congruent sides

7. Could an isosceles triangle be equilateral?
So is an equilateral triangle always isosceles… or an isosceles triangle always an equilateral triangle?

8. Classify the following as equilateral, isosceles, or scalene.

9. Triangle JKM is an equilateral triangle with all sides 0.75 units.
If point M is the midpoint of JL, classify triangle JKM as equilateral, isosceles, or scalene. Explain your reasoning.
Find JM.
0.75
0.75
M is the midpoint.
0.75
JM + ML = JL
JM + JM = 1.5
Def. Of Midpoint
2(JM) = 1.5
JM = 0.75
Triangle JKM is an equilateral triangle with all
sides 0.75 units.

10. Isosceles since two sides are congruent (0.75).
Classify triangle KML as equilateral, isosceles, or scalene. Explain your reasoning.
Isosceles since two sides are congruent (0.75).

11. Find the measures of the sides of isosceles triangle ABC.
4x + 1 = 5x – 0.5
Since the figure shows the sides equal
1 = x – 0.5
1.5 = x
AC = 7
BC = 7
AB = 12.5
AC = 4x + 1= 4(1.5) + 1 = 7
BC = 5x – 0.5 = 5(1.5) – 0.5 = 7
AB = 9x – 1 = 9(1.5) – 1 = 12.5

12. Find the measures of the sides of equilateral triangle FGH.
Since all sides are equal any 2
of the 3 sides can be set equal.
2y + 5 = 3y – 3
5 = y – 3
8 = y
FG = FH = GH = 21
FG = 2y + 5 = 2(8) + 5 = 21
FH = 5y – 19 = 5(8) – 19 = 21
GH = 3y – 3 = 3(8) – 3 = 21

13. Homework
Pg – 14 all, 16 – 44 EOE, 78 – 84 E