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Understanding Scalene and Isosceles Triangles: Types and Classifications

This guide covers the classification of triangles into various types, focusing on scalene and isosceles triangles. It explains the characteristics of isosceles triangles, which have at least two congruent sides, and scalene triangles, where no sides are congruent. Additionally, the types of triangles based on angles—like acute, obtuse, and right triangles—are discussed. The section includes sample problems for classification and calculations, making it an excellent resource for students learning geometry.

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Understanding Scalene and Isosceles Triangles: Types and Classifications

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  1. Types of Triangles 3.6 AlexaBolock Mod. 9

  2. Scalene and Isosceles Triangles Isosceles- is a triangle in which at least two sides are congruent. Scalene- is a triangle in which no two sides are congruent.

  3. Equilateral and Equiangular Triangles • Equiangular- is a triangle in which all angles are congruent. • Equilateral- is a triangle in which all sides are congruent.

  4. Acute and Obtuse Triangles Obtuse Acute • Triangle in which all angles are acute. • Triangle in which one of the angles is an obtuse angle.

  5. Right Triangle • A Right triangle is a triangle in which one of the angles is a right angle. • The side opposite the right angle is called the hypotenuse. • The sides that form the right angle are called the legs.

  6. Sample Problems

  7. Sample Problems cont.

  8. Practice Problems 1. Classify each of the triangles as scalene, isosceles, or equilateral. a.) b.) c.) X 6 6 PX> XN XN=PN P N 6

  9. Practice Problems 2. Classify each triangle as acute, right, or obtuse. • a.) b.) • c.) d.) Y 80° 60 ° 40° Z X

  10. Practice Problems 3. If PGK is equilateral, what are the values of x and y? P 15 X+8 K G 1/3 y – 6

  11. Practice Problems 4. S Proof E N A B

  12. Practice Problem 5. A C B

  13. Answers to Practice Problems 1. • a.) Equilateral • b.) Isosceles • c.) Scalene 2. a.) Right b.) Obtuse c.) Acute d.) Right 3. X+8=15 X=7 1/3y-6=15 Y-18=45 Y=63

  14. Answers cont. • 4.

  15. Answers cont. 5. • 13+x+4+x+7=42 • 24+2x=42 • 2x=42-24 • 2x=18 • X=9 • AB= 13 • AC=9+7=16 • BC=x+4=13 13=13 So the triangle is isos.

  16. Other Helpful Links • http://www.emints.org/ethemes/resources/S00000371.shtml • http://www.regentsprep.org/regents/math/triang/LTriangle.htm • Triangle song by James Blunt • http://www.youtube.com/watch?v=o2Z6tDSb6c8&feature=related

  17. Works Cited Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougall Littel and Company, 2004. 142-147. "Types of Triangles." 2008. Oswego City School District Regents Exam Prep Center. 28 May 2008 <http://www.regentsprep.org/regents/math/triang/LTriangle.htm>.

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