geometry section 4-1 1112
DESCRIPTION
Classifying TrianglesTRANSCRIPT
![Page 1: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/1.jpg)
Chapter 4Congruent Triangles
Monday, January 30, 2012
![Page 2: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/2.jpg)
Section 4-1Classifying Triangles
Monday, January 30, 2012
![Page 3: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/3.jpg)
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
![Page 4: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/4.jpg)
Vocabulary
1. Acute Triangle:
2. Equiangular Triangle:
3. Obtuse Triangle:
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012
![Page 5: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/5.jpg)
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
![Page 6: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/6.jpg)
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
![Page 7: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/7.jpg)
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
![Page 8: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/8.jpg)
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
![Page 9: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/9.jpg)
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
![Page 10: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/10.jpg)
Vocabulary
6. Isosceles Triangle:
7. Scalene Triangle:
Monday, January 30, 2012
![Page 11: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/11.jpg)
Vocabulary
6. Isosceles Triangle: A triangle in which at least two sides have the same measure
7. Scalene Triangle:
Monday, January 30, 2012
![Page 12: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/12.jpg)
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
![Page 13: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/13.jpg)
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Monday, January 30, 2012
![Page 14: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/14.jpg)
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular
Monday, January 30, 2012
![Page 15: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/15.jpg)
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular Obtuse
Monday, January 30, 2012
![Page 16: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/16.jpg)
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Monday, January 30, 2012
![Page 17: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/17.jpg)
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Right
Monday, January 30, 2012
![Page 18: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/18.jpg)
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Right
m∠XYW +m∠WYZ
Monday, January 30, 2012
![Page 19: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/19.jpg)
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
![Page 20: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/20.jpg)
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
![Page 21: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/21.jpg)
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
![Page 22: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/22.jpg)
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
![Page 23: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/23.jpg)
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
JKO is right
m∠JNM >90°
Monday, January 30, 2012
![Page 24: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/24.jpg)
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
JKO is right
m∠JNM >90°
m∠JKO =90°
Monday, January 30, 2012
![Page 25: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/25.jpg)
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
JKO is right OLN is equiangular
m∠JNM >90°
m∠JKO =90°
Monday, January 30, 2012
![Page 26: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/26.jpg)
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
JKO is right OLN is equiangular
m∠JNM >90°
m∠JKO =90° All 3 angles have the same measureMonday, January 30, 2012
![Page 27: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/27.jpg)
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
![Page 28: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/28.jpg)
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 threesides of ∆VWY have different measures, thus making ∆VWY a scalene triangle.
Monday, January 30, 2012
![Page 29: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/29.jpg)
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
Monday, January 30, 2012
![Page 30: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/30.jpg)
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
Monday, January 30, 2012
![Page 31: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/31.jpg)
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12− d = 4d −13
Monday, January 30, 2012
![Page 32: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/32.jpg)
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
![Page 33: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/33.jpg)
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
![Page 34: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/34.jpg)
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
![Page 35: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/35.jpg)
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
![Page 36: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/36.jpg)
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
![Page 37: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/37.jpg)
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
MK = 4d −13
Monday, January 30, 2012
![Page 38: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/38.jpg)
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
MK = 4d −13
MK = 4(5)−13
Monday, January 30, 2012
![Page 39: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/39.jpg)
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
MK = 4d −13
MK = 4(5)−13
MK =20−13=7 units
Monday, January 30, 2012
![Page 40: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/40.jpg)
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
MK = 4d −13
MK = 4(5)−13
MK =20−13=7 units
KL = d +6
Monday, January 30, 2012
![Page 41: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/41.jpg)
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
MK = 4d −13
MK = 4(5)−13
MK =20−13=7 units
KL = d +6
KL =5+6
Monday, January 30, 2012
![Page 42: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/42.jpg)
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
MK = 4d −13
MK = 4(5)−13
MK =20−13=7 units
KL = d +6
KL =5+6
KL =11 units
Monday, January 30, 2012
![Page 43: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/43.jpg)
Check Your Understanding
Peruse the following problems: p. 238 #1-14
Monday, January 30, 2012
![Page 44: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/44.jpg)
Problem Set
Monday, January 30, 2012
![Page 45: Geometry section 4-1 1112](https://reader031.vdocuments.site/reader031/viewer/2022020306/54b2ba324a7959954b8b45cc/html5/thumbnails/45.jpg)
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