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Exploring Triangle Varieties: Types and Properties

Discover the different types of triangles based on sides and angles with detailed explanations and proofs. Dive into scalene, isosceles, equilateral, acute, right, and obtuse triangles. Solve problems using triangle parts and properties.

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Exploring Triangle Varieties: Types and Properties

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  1. Types of Triangle Objective- name the various types of triangles and their parts. Chapter 3.6

  2. Triangles by sides: Scalene- a scalene triangle is triangle in whichno two sides are congruent W D A

  3. G U M Isosceles-an isosceles triangle is a triangle in whichat least 2 sides are congruent

  4. Equilateral- an equilateral triangle is a triangle inwhich all sides are congruent Y U M

  5. Triangles by angles: Acute: An acute triangle is a triangle in which all angles are acute and add up to 180 degrees. D 80 60 40 R E

  6. Right: A right triangle is a triangle in which one of the angles is a right angle. H O T

  7. Obtuse: An obtuse triangle is a triangle in which ONE of the angles is an obtuse angle. F 30 110 40 N I

  8. D Given: AD and CD are legs of isosceles ADC. B is the midpoint of AC Prove: A  C A C B • AD and CD are legs of isosceles ADC. • AD  CD • B is midpt. of AC • AB  BC • Draw DB • DB  DB • DAB  DCB •  A  C • Given • An isos. triangle is a triangle in which at least 2 sides are . • Given • A mdpt. divides a seg into 2  segs. • 2 points determine a line. • Reflexive Property • SSS • CPCTC

  9. Given: AB = x + 3 AC = 3x + 2 BC = 2x + 3 Perimeter of ABC = 20 Show that ABC is scalene. A B C Perimeter = 20 = x + 3 + 3x + 2 + 2x + 3 20 = 6x + 8 12 = 6x 2 = x AB = 2 + 3 = 5 AC = 3(2) + 2 = 8 BC = 2(2) + 3 = 7 ABC is scalene because no sides are .

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