1. T YPES OF T RIANGLES Section 3.6 Kory and Katrina Helcoski

2. C LASSIFYING T RIANGLES B Y S IDES Scalene- a triangle in which no two sides are congruent AB=7 BC=10 CA=8

3. C LASSIFYING T RIANGLES B Y S IDES Isosceles- a triangle in which at least 2 sides are congruent The legs of an isosceles triangle are congruent <A and <C are called base angles and <B is called the vertex angle AB= 10 BC= 10 AC= 5

4. C LASSIFYING T RIANGLES B Y S IDES Equilateral- a triangle in which all sides are congruent An equilateral triangle is also and isosceles triangle. AB=7 BC=7 CA=7

5. C LASSIFYING T RIANGLES B Y S IDES Triangle Video (Microsoft PowerPoint was not allowing us to attach the video to it, see other attachment from E-Mail)

6. C LASSIFYING T RIANGLES B Y A NGLES Equiangular- a triangle in which all angles are acute and congruent <ABC = 60 ° <BCA = 60 ° <CAB = 60 ° An equiangular triangle is also an equilateral triangle and vice versa.

7. C LASSIFYING T RIANGLES B Y A NGLES Acute triangle- a triangle in which all angles are acute. <ABC=50 ° <BCA=70 ° <CAB=60 °

8. C LASSIFYING T RIANGLES B Y A NGLES Right Triangle- a triangle in which one of the angles is a right angle hypotenuse > either leg Pythagorean Theorem- leg² + leg² = hyp² <ACB is a right angle (90°)

9. C LASSIFYING T RIANGLES B Y A NGLES Obtuse Triangle- a triangle in which one of the sides is an obtuse angle <ABC= 40 ° <ACB=110 ° <BAC=30 °

10. S AMPLE P ROBLEMS Given: <BCD=80 ° Prove: Δ ABC is obtuse Proof: <BCD= 80° and <ACD is a straight angle, which is 180 °, so <ACB is 100 ° by subtraction. Since Δ ABC contains an obtuse angle it is an obtuse triangle.

11. S AMPLE P ROBLEMS 1. 1. given 2. <1 <2 2. given 3. F is the mdpt of 3. given 4. 4. mdpts divide segs into 2 segs 5. ΔDAF ΔECF 5. SAS (1,2,4) 6. <DAF <ECF 6. CPCTC 7. ΔABC is isos 7. If 2 angles of the Δ are, the Δ is isos <1 <2 F is the mdpt of Prove: ΔABC is isos

12. P RACTICE P ROBLEMS If Δ ABC is equilateral, what are the values of x and y?

13. P RACTICE P ROBLEMS ( ANSWER ) x + 6=8 x = 2 y =15

14. P RACTICE P ROBLEMS Given: ΔABC is an isosceles triangle with base D is the midpoint of Prove: <A <C

15. P RACTICE P ROBLEMS ( ANSWER ) Statements Reasons 1.ΔABC is an isosceles 1. Given Triangle with base 2. D is the midpoint of 2. Given 3. 3. If a point is the midpoint of a segment, then it divides the segment into two congruent segments 4. 4. legs of an isosceles triangle are congruent 5. 5. Reflexive Property 6. ΔABD ΔCBD 6. SSS (3, 4, 5) 7. <A <C 7. CPCTC

16. W ORKS C ITED P AGE Rhoad, Richard, George Milauskas, and Robert Whipple. "3.6- Types of Triangles." Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1991. 142-147. Print.