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3.6 Types of Triangles Objectives:
Name the various types of triangles and their parts Use different types of triangles in proofs
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scalene triangle: a triangle with no two sides congruent.
B C isosceles triangles: a triangle with at least two sides congruent. Proof reasons: If , then The converse of this is true as well!!!! A B C vertex angle legs legs base base angles
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equilateral triangle: a triangle with all sides congruent.
B C equiangular triangle: a triangle with all angles congruent. A B C
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acute triangle: a triangle with all acute angles.
B C right triangle: a triangle with a right angle. A B C hypotenuse leg leg
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obtuse triangle: a triangle with an obtuse angle.
C
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______________ _____________ triangle
Naming triangles: Example 1: a) 40° 70° 70° ______________ _____________ triangle angle name side name
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______________ _____________ triangle
b) ______________ _____________ triangle angle name side name
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______________ _____________ triangle
c) ______________ _____________ triangle angle name side name 70° 60° 50°
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______________ _____________ triangle
d) ______________ _____________ triangle angle name side name
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______________ _____________ triangle
angle name side name 120° 30° 30°
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______________ _____________ triangle
f) ______________ _____________ triangle angle name side name
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Isosceles Example 2: Scalene, Isosceles, or Equilateral?
Perimeter = 94 units 8x +10 7x – 2 x2 +10 Isosceles
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Example 2: E D A C B Statements Reasons 1. 2. 3. 4. 5. 6. 7. 8. AED CDE Given BED BDE Given Reflexive Property ∆ADE ∆CED ASA CPCTC Given Subtraction Property ∆EBD is isosceles Definition of isosceles
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All right angles are congruent
Q S T U Example 3: Statements Reasons 1. 2. 3. 4. 5. 6. 7. 8. Given Given Given QTS and RST are right angles Definition of perpendicular lines QTS RST All right angles are congruent Reflexive Property ∆QTS ∆RST SAS CPCTC Continued on next slide
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Definition of isosceles
R Q S T U Example 3: Statements Reasons 9. 10. 11. 12. Given Definition of isosceles Subtraction Property Definition of isosceles
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A Example 4: F B E D C Statements Reasons 1. 2. 3. 4. 5. 6. 7. 8. Given Definition of equilateral Definition of equiangular AEF is supp. to AED Linear Pair Postulate ACB is supp. to ACD Linear Pair Postulate AEF ACB Congruent Supplements Thm. Definition of equilateral Given Continued on next slide
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A Example 4: F B E D C Statements Reasons 9. 10. 11. ∆AEF ∆ACB SAS CPCTC Definition of isosceles
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