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3.2A –Properties of Triangles

3.2A –Properties of Triangles . Geometry Notes T.2.G.2 Investigate the measures of segments to determine the existence of triangles ( triangle inequality theorem )

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3.2A –Properties of Triangles

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  1. 3.2A –Properties of Triangles Geometry Notes T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem) CGT.5.G.3 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

  2. Naming Triangles • Always name triangles by their vertices B A C

  3. Properties of Triangles • Largest side across from largest angle • Smallest side across from smallest angle

  4. 85o C 32o 63o T A Example • In the following triangle, list the sides in order from smallest to largest.

  5. G 5 in U 6 in 4in M Now You Try… • In the following triangle, list the angles in order from largest to smallest

  6. Triangle Inequality Theorem • The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 3+4 >5 3+5 > 4 4+5 > 3 5 in. 4 in. 3 in.

  7. Examples • Can a triangle have sides with the given lengths? Explain. 5inches, 7 inches, 15 inches No. 5 + 7 ≯ 15 • Can a triangle have sides with the given lengths? Explain. 12 cm, 20 cm, 15 cm Yes. 12 + 15 > 20

  8. Now You Try… • Can a triangle have sides with the given lengths? Explain. 8 m, 12 m, 4 m No. 8 + 4 ≯ 12

  9. Example • The lengths of two sides of a triangle are given. Describe the possible lengths for the third side. 5 feet, 12 feet 7 < x < 17

  10. Now You Try… • The lengths of two sides of a triangle are given. Describe the possible lengths of the third side. 18 mm, 24 mm 24 – 18 = 6 6 < x < 42 24 + 18 = 42

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