1. Classifying Triangles
4-1
Classifying Triangles
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3. right 3.
4. If the perimeter is 47, find x and the lengths of the three sides.
right
acute
obtuse
x = 5; 8; 16; 23

3. Objectives
Classify triangles by their angle measures and side lengths.
Use triangle classification to find angle measures and side lengths.

4. Vocabulary acute triangle equiangular triangle right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle

5. Recall that a triangle ( ) is a polygon with three sides
Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

6. C A B AB, BC, and AC are the sides of ABC.
A, B, C are the triangle's vertices.

7. Acute Triangle Three acute angles Triangle Classification
By Angle Measures
Acute Triangle
Three acute angles

8. Three congruent acute angles
Triangle Classification
By Angle Measures
Equiangular Triangle
Three congruent acute angles

9. Right Triangle One right angle Triangle Classification
By Angle Measures
Right Triangle
One right angle

10. Obtuse Triangle One obtuse angle Triangle Classification
By Angle Measures
Obtuse Triangle
One obtuse angle

11. Class Example: Classifying Triangles by Angle Measures
Classify BDC by its angle measures.
B is an obtuse angle.
B is an obtuse angle. So BDC is an obtuse triangle.

12. Class Example: Classifying Triangles by Angle Measures
Classify ABD by its angle measures.
ABD and CBD form a linear pair, so they are supplementary.
Therefore mABD + mCBD = 180°. By substitution, mABD + 100° = 180°. So mABD = 80°. ABD is an acute triangle by definition.

13. Example 1 - 3
Classify EHG, EFH, FHG by its angle measure
Triangle EHG is right
Triangle EFH is obtuse
Triangle FHG is equiangular

14. Equilateral Triangle Three congruent sides Triangle Classification
By Side Lengths
Equilateral Triangle
Three congruent sides

15. At least two congruent sides
Triangle Classification
By Side Lengths
Isosceles Triangle
At least two congruent sides

16. Scalene Triangle No congruent sides Triangle Classification
By Side Lengths
Scalene Triangle
No congruent sides

17. Remember!
When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

18. Class Example: Classifying Triangles by Side Lengths
Classify EHF by its side lengths.
From the figure, So HF = 10, and EHF is isosceles.

19. Class Example: Classifying Triangles by Side Lengths
Classify EHG by its side lengths.
By the Segment Addition Postulate, EG = EF + FG = = 14. Since no sides are congruent, EHG is scalene.

20. Example # 1 - 3
Classify ABC, ABD and ACD by its side lengths.
ABC = equilateral Triangle ABD = Scalene
Triangle ACD = scalene

21. Example # 1: Using Triangle Classification
Find the side lengths of JKL.
Step 1 Find the value of x.
JK = KL
4x – 1.3 = x + 3.2
3x = 4.5
x = 1.5

22. Example #1 Continued
Find the side lengths of JKL.
Step 2 Substitute 1.5 into the expressions to find the side lengths.
JK = 4x – 1.3
= 4(1.5) – 1.3 = 4.7
KL = x + 3.2
= 1(1.5) = 4.7
JL = 5x + 0.2
= 5(1.5) +0.2 = 7.3

23. Example # 2
Find the side lengths of equilateral FGH.
Step 1 Find the value of y.
Given.
FG = GH = FH
Def. of  segs.
Substitute
(3y – 4) for FG and (2y + 3) for GH.
3y – 4 = 2y + 3
Add 4 and subtract 2y from both sides.
y = 7

24. Check It Out! Example #2 Continued
Find the side lengths of equilateral FGH.
Step 2 Substitute 7 into the expressions to find the side lengths.
FG = 3y – 4
= 3(7) – 4 = 17
GH = 2y + 3
= 2(7) + 3 = 17
FH = 5y – 18
= 5(7) – 18 = 17

25. Homework:
Page 219: # 1-19

26. 4. Find the side lengths of the triangle. acute; equilateral
Exit Question
Classify each triangle by its angles and sides.
MNQ
NQP
MNP
4. Find the side lengths of the triangle.
acute; equilateral
obtuse; scalene
acute; scalene
29; 29; 23

27. 4. Find the side lengths of the triangle.
Exit Question Name:
Classify each triangle by its angles and sides.
MNQ
NQP
MNP
4. Find the side lengths of the triangle.

28. 4. Find the side lengths of the triangle.
Exit Question Name:
Classify each triangle by its angles and sides.
MNQ
NQP
MNP
4. Find the side lengths of the triangle.