Classifying Triangles

1. Chapter 4
Congruent Triangles
Monday, January 30, 2012

2. Section 4-1
Classifying Triangles
Monday, January 30, 2012

3. Essential Questions
How do you identify and classify triangles by angle measures?
How do you identify and classify triangles by side measures?
Monday, January 30, 2012

4. Vocabulary
1. Acute Triangle:
2. Equiangular Triangle:
3. Obtuse Triangle:
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012

5. Vocabulary
1. Acute Triangle: A triangle in which all three angles have a measure
of less than 90 degrees
2. Equiangular Triangle:
3. Obtuse Triangle:
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012

6. Vocabulary
1. Acute Triangle: A triangle in which all three angles have a measure
of less than 90 degrees
2. Equiangular Triangle: A triangle in which all three angles have a
measure of 60 degrees, thus making them all equal
3. Obtuse Triangle:
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012

7. Vocabulary
1. Acute Triangle: A triangle in which all three angles have a measure
of less than 90 degrees
2. Equiangular Triangle: A triangle in which all three angles have a
measure of 60 degrees, thus making them all equal
3. Obtuse Triangle: A triangle in which one of the angles has a measure
greater than 90 degrees
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012

8. Vocabulary
1. Acute Triangle: A triangle in which all three angles have a measure
of less than 90 degrees
2. Equiangular Triangle: A triangle in which all three angles have a
measure of 60 degrees, thus making them all equal
3. Obtuse Triangle: A triangle in which one of the angles has a measure
greater than 90 degrees
4. Right Triangle: A triangle in which one of the angles has a measure of
90 degrees
5. Equilateral Triangle:
Monday, January 30, 2012

9. Vocabulary
1. Acute Triangle: A triangle in which all three angles have a measure
of less than 90 degrees
2. Equiangular Triangle: A triangle in which all three angles have a
measure of 60 degrees, thus making them all equal
3. Obtuse Triangle: A triangle in which one of the angles has a measure
greater than 90 degrees
4. Right Triangle: A triangle in which one of the angles has a measure of
90 degrees
5. Equilateral Triangle: A triangle in which all three sides have the same
measure
Monday, January 30, 2012

10. Vocabulary
6. Isosceles Triangle:
7. Scalene Triangle:
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11. Vocabulary
6. Isosceles Triangle: A triangle in which at least two sides have the
same measure
7. Scalene Triangle:
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12. Vocabulary
6. Isosceles Triangle: A triangle in which at least two sides have the
same measure
7. Scalene Triangle: A triangle in which no two sides have the same
measure
Monday, January 30, 2012

13. Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
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14. Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular
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15. Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular Obtuse
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16. Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your
reasoning.
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17. Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your
reasoning.
Right
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18. Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your
reasoning.
Right
m∠XYW + m∠WYZ
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19. Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your
reasoning.
Right
m∠XYW + m∠WYZ
= 40°+50° = 90°
Monday, January 30, 2012

20. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
Monday, January 30, 2012

21. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
Monday, January 30, 2012

22. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
m∠JNM > 90°
Monday, January 30, 2012

23. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
m∠JNM > 90°
JKO is right
Monday, January 30, 2012

24. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
m∠JNM > 90°
JKO is right
m∠JKO = 90°
Monday, January 30, 2012

25. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
m∠JNM > 90°
JKO is right OLN is equiangular
m∠JKO = 90°
Monday, January 30, 2012

26. Example 3
The triangular truss is modeled for steel construction. Classify ∆JMN,
∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your
reasoning. This figure is drawn to scale.
JMN is obtuse
m∠JNM > 90°
JKO is right OLN is equiangular
m∠JKO = 90° All 3 angles have the same measure
Monday, January 30, 2012

27. Example 4
If point Y is the midpoint of VX and WY = 3 in., classify ∆VWY as
equilateral, isosceles, or scalene. Explain your reasoning.
Monday, January 30, 2012

28. Example 4
If point Y is the midpoint of VX and WY = 3 in., classify ∆VWY as
equilateral, isosceles, or scalene. Explain your reasoning.
∆VWY is scalene. Since Y is the midpoint of VX,
we know that VY = YX = .5(VX) = 4.2 in. Along
with the fact that WY = 3 in., we know all three
sides of ∆VWY have different measures, thus
making ∆VWY a scalene triangle.
Monday, January 30, 2012

29. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
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30. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
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31. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
Monday, January 30, 2012

32. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
Monday, January 30, 2012

33. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
Monday, January 30, 2012

34. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d
Monday, January 30, 2012

35. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d
ML =12 −5
Monday, January 30, 2012

36. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d
ML =12 −5
ML = 7 units
Monday, January 30, 2012

37. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13
ML =12 −5
ML = 7 units
Monday, January 30, 2012

38. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13
ML =12 −5 MK = 4(5)−13
ML = 7 units
Monday, January 30, 2012

39. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13
ML =12 −5 MK = 4(5)−13
ML = 7 units MK = 20 −13 = 7 units
Monday, January 30, 2012

40. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13 KL = d + 6
ML =12 −5 MK = 4(5)−13
ML = 7 units MK = 20 −13 = 7 units
Monday, January 30, 2012

41. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13 KL = d + 6
ML =12 −5 MK = 4(5)−13 KL = 5+ 6
ML = 7 units MK = 20 −13 = 7 units
Monday, January 30, 2012

42. Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12 − d = 4d −13
25 = 5d
d =5
ML =12 − d MK = 4d −13 KL = d + 6
ML =12 −5 MK = 4(5)−13 KL = 5+ 6
ML = 7 units MK = 20 −13 = 7 units KL =11 units
Monday, January 30, 2012

43. Check Your Understanding
Peruse the following problems: p. 238 #1-14
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44. Problem Set
Monday, January 30, 2012

45. Problem Set
p. 239 #15-51 odd (skip 39), 56, 60, 75
“ Do not listen to those who weep and complain, for their disease is
contagious.” - Og Mandino
Monday, January 30, 2012