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Chapter 4Congruent Triangles
Monday, January 30, 2012
Section 4-1Classifying Triangles
Monday, January 30, 2012
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
Vocabulary
1. Acute Triangle:
2. Equiangular Triangle:
3. Obtuse Triangle:
4. Right Triangle:
5. Equilateral Triangle:
Monday, January 30, 2012
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
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
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
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
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
Vocabulary
6. Isosceles Triangle:
7. Scalene Triangle:
Monday, January 30, 2012
Vocabulary
6. Isosceles Triangle: A triangle in which at least two sides have the same measure
7. Scalene Triangle:
Monday, January 30, 2012
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
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Monday, January 30, 2012
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular
Monday, January 30, 2012
Example 1
Classify each triangle as acute, equiangular, obtuse, or right.
a. b.
Equiangular Obtuse
Monday, January 30, 2012
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Monday, January 30, 2012
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Right
Monday, January 30, 2012
Example 2
Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Right
m∠XYW +m∠WYZ
Monday, January 30, 2012
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
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
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
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
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
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
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
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
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
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
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
Monday, January 30, 2012
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
Monday, January 30, 2012
Example 5
Find the measure of the sides of isosceles ∆KLM with base KL.
ML = MK
12− d = 4d −13
Monday, January 30, 2012
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
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
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
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
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
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
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
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
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
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
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
Check Your Understanding
Peruse the following problems: p. 238 #1-14
Monday, January 30, 2012
Problem Set
Monday, January 30, 2012
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