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Types of Triangles

Types of Triangles. Section 3.6 Kory and Katrina Helcoski. Classifying Triangles By Sides. Scalene- a triangle in which no two sides are congruent AB=7 BC=10 CA=8. Classifying Triangles By Sides. Isosceles- a triangle in which at least 2 sides are congruent

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Types of Triangles

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  1. Types of Triangles Section 3.6 Kory and Katrina Helcoski

  2. Classifying Triangles By Sides • Scalene- a triangle in which no two sides are congruent • AB=7 • BC=10 • CA=8

  3. Classifying Triangles By Sides • 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. Classifying Triangles By Sides • Equilateral- a triangle in which all sides are congruent • An equilateral triangle is also and isosceles triangle. • AB=7 • BC=7 • CA=7 WOW

  5. Classifying Triangles By Sides • Triangle Video (Microsoft PowerPoint was not allowing us to attach the video to it, see other attachment from E-Mail)

  6. Classifying Triangles By Angles • 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. Classifying Triangles By Angles • Acute triangle- a triangle in which all angles are acute. • <ABC=50° • <BCA=70° • <CAB=60°

  8. Classifying Triangles By Angles • 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. Classifying Triangles By Angles • Obtuse Triangle- a triangle in which one of the sides is an obtuse angle • <ABC= 40° • <ACB=110° • <BAC=30°

  10. Sample Problems • Given: <BCD=80° • Prove:ΔABC is obtuse • Proof: <BCD= 80° and <ACD is a straight angle, which is 180°, so <ACB is 100° by subtraction. Since ΔABC contains an obtuse angle it is an obtuse triangle.

  11. Sample Problems <1 <2 F is the mdpt of Prove: ΔABC is isos 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 100%

  12. Practice Problems If ΔABC is equilateral, what are the values of x and y?

  13. Practice Problems (answer) x + 6=8 x = 2 y =15

  14. Practice Problems • Given: ΔABC is an isosceles triangle with base D is the midpoint of Prove: <A <C

  15. Practice Problems (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. Works Cited Page Rhoad, Richard , George Milauskas , and Robert Whipple . "3.6- Types of Triangles ." Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1991. 142-147. Print.

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