1. 4-1: Classifying Triangles
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4-1: Classifying Triangles

2. Classifying Triangles
Section 4–1
Geometry PreAP, Revised ©2013
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4-1: Classifying Triangles

3. Triangle Classification
Triangles are polygons with three sides. They are classified by their angle measures and side lengths
Angle Measure
Acute Triangle has three acute angles
Equiangular Triangle has three congruent acute angles
Right Triangle has one right angle
Obtuse Triangle has one obtuse angle
Side Lengths
Equilateral Triangle has three congruent sides
Isosceles Triangle has at least two congruent sides
Scalene Triangle has no congruent sides
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4-1: Classifying Triangles

4. Classifying TrianglesB A C
Sides: 𝑨𝑩 , 𝑩𝑪 , and 𝑨𝑪 are the sides of ΔABC
A, B, C are the triangle's vertices
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4-1: Classifying Triangles

5. 4-1: Classifying Triangles
Example 1
Classify ΔFHG by its angle measures and identify the name.
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4-1: Classifying Triangles

6. 4-1: Classifying Triangles
Your Turn
Classify ΔFHE by its angle measures and identify the name.
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4-1: Classifying Triangles

7. 4-1: Classifying Triangles
Example 2
Draw an isosceles right angle. If a picture is not possible, explain why.
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4-1: Classifying Triangles

8. 4-1: Classifying Triangles
Example 3
Draw an scalene equiangular. If a picture is not possible, explain why.
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4-1: Classifying Triangles

9. 4-1: Classifying Triangles
Your Turn
Draw an scalene right angle. If a picture is not possible, explain why.
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4-1: Classifying Triangles

10. 4-1: Classifying Triangles
Example 4
Classify ΔEHF by its side lengths, the length of 𝑯𝑭 and identify the name.
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4-1: Classifying Triangles

11. 4-1: Classifying Triangles
Example 5
Classify ΔEHG by its side lengths, the length of 𝑯𝑭 and identify the name.
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4-1: Classifying Triangles

12. 4-1: Classifying Triangles
Your Turn
Classify ΔADB by its side lengths, the length of 𝑨𝑪 and identify the name.
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4-1: Classifying Triangles

13. 4-1: Classifying Triangles
Example 6
Find the side lengths of ΔJKL, identify the type of triangle, and provide a two-column proof
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4-1: Classifying Triangles

14. 4-1: Classifying Triangles
Example 6 (Proof)
Find the side lengths of ΔJKL, identify the type of triangle, and provide a two-column proof
Statements
Reasons
1) 𝑱𝑲 ≅ 𝑲𝑳
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
4) 4x = 2x + 17
-2x -2x
Addition POE
5) 2x = 17
Subtraction POE
6) x = 8.5
Division POE
7) JK = 4(8.5) = 23.3
KL = 2(8.5) = 23.3
JL = 5(8.5) + 2 = 44.5
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
4) 4x = 2x + 17
-2x -2x
Addition POE
5) 2x = 17
Subtraction POE
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
4) 4x = 2x + 17
-2x -2x
Addition POE
5) 2x = 17
Subtraction POE
6) x = 8.5
Division POE
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
4) 4x = 2x + 17
-2x -2x
Addition POE
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
4) 4x = 2x + 17
-2x -2x
Addition POE
5) 2x = 17
Subtraction POE
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
2) JK = KL
Definition of Congruency
3) 4x – 10.7 = 2x + 6.3
Substitution
Statements
Reasons
1) 𝐽𝐾 ≅ 𝐾𝐿
Given
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4-1: Classifying Triangles

15. 4-1: Classifying Triangles
Your Turn
Find the side lengths of equilateral ΔFGH and provide a two-column proof
Statements
Reasons
1) 𝑭𝑮 ≅ 𝑮𝑯 ≅ 𝑭𝑯
Given
2) FG = GH = FH
Definition of Congruency
3) FG = GH
4) 3y – 4 = 2y + 3
Substitution
5) 3y = 2y + 7
-2y -2y
Addition POE
6) y = 7
Subtraction POE
7) FG = 3(7) – 4 = 17
GH = 2(7) + 3 = 17
FH = 5(7) – 18 = 17
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4-1: Classifying Triangles

16. 4-1: Classifying Triangles
Assignment
Page , all, 35-37
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4-1: Classifying Triangles