3.6 Types of Triangles Objectives: Name the various types of triangles and their parts Use different types of triangles in proofs

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

equilateral triangle: a triangle with all sides congruent. B C equiangular triangle: a triangle with all angles congruent. A B C

acute triangle: a triangle with all acute angles. B C right triangle: a triangle with a right angle. A B C hypotenuse leg leg

obtuse triangle: a triangle with an obtuse angle. C

______________ _____________ triangle Naming triangles: Example 1: a) 40° 70° 70° ______________ _____________ triangle angle name side name

______________ _____________ triangle b) ______________ _____________ triangle angle name side name

______________ _____________ triangle c) ______________ _____________ triangle angle name side name 70° 60° 50°

______________ _____________ triangle d) ______________ _____________ triangle angle name side name

______________ _____________ triangle angle name side name 120° 30° 30°

______________ _____________ triangle f) ______________ _____________ triangle angle name side name

Isosceles Example 2: Scalene, Isosceles, or Equilateral? Perimeter = 94 units 8x +10 7x – 2 x2 +10 Isosceles

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

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

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

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

A Example 4: F B E D C Statements Reasons 9. 10. 11. ∆AEF  ∆ACB SAS CPCTC Definition of isosceles