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Name the angles opposite of each side:

Y. X. Z. Name the angles opposite of each side:. X is opposite of YZ Y is opposite of XZ Z is opposite of XY. Triangle Inequalities. Geometry. Draw a triangle. Measure all the sides of the triangle. Add any two sides together and compare it to the third. What do you notice?

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Name the angles opposite of each side:

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  1. Y X Z Name the angles opposite of each side: • X is opposite of YZ • Y is opposite of XZ • Z is opposite of XY

  2. Triangle Inequalities Geometry

  3. Draw a triangle • Measure all the sides of the triangle. • Add any two sides together and compare it to the third. What do you notice? • See if your conjecture is true for all three cases.

  4. Y X Z Triangle Inequality Theorem • The sum of the length of any two sides of a triangle is greater than the third side. • XY + YZ > XZ • YZ + XZ > XY • XZ + XY > YZ

  5. Using the Triangle Inequality Theorem… • Is it possible for 3, 7, and 8 to be the sides of a triangle? • What about 3, 6, and 10?

  6. Back To The Triangles • Measure the angles of the triangle you had drawn. • Compare the angle measurement and the measurement of the opposite side with the others. • What do you notice?

  7. Y X Z Inequalities Relating Sides and Angles • Theorem 4-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. • Ex. If XZ > XY,then mY > mZ

  8. Y X Z Inequalities Relating Sides and Angles • Theorem 4-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. • Ex. If mY > mZ,then XZ > XY

  9. In TUV, Name the sides from shortest to longest T • TV, UV, UT 58 62 U V

  10. Homework Work Packet: Triangle Inequalities

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