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Chapter 7

Chapter 7. Triangle Inequalities. Section 7-1. Segments, Angles and Inequalities. Comparison Property. For any two real numbers, a and b, exactly one of the following statements is true. a<b a = b a b. Theorem 7-1.

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Chapter 7

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  1. Chapter 7 Triangle Inequalities

  2. Section 7-1 Segments, Angles and Inequalities

  3. Comparison Property • For any two real numbers, a and b, exactly one of the following statements is true. a<b a = b ab

  4. Theorem 7-1 • If point C is between points A and B, and A, C, and B are collinear, then AB AC and ABCB.

  5. Theorem 7-2 • If EP is between ED and EF, then mDEF mDEPand mDEF mPEF.

  6. Transitive Property • If a<b and b<c, then a<c. • If ab and bc, then ac.

  7. Addition and Subtraction Properties • If a<b, then a + c<b + c and a - c<b – c • If ab, then a + cb + c and a - cb – c

  8. Multiplication and Division Properties • If c0 and a<b, then ac<bc and a/c<b/c • If c 0 and a b, then ac bc and a/c b/c

  9. Section 7-2 Exterior Angle Theorem

  10. Exterior Angle • An angle that forms a linear pair with one of the angles of a triangle

  11. Remote Interior Angles • The two angles in a triangle that do not form a linear pair with the exterior angle

  12. Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

  13. Exterior Angle Inequality Theorem • The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles.

  14. Theorem 7-5 • If a triangle has one right angle, then the other two angles must be acute.

  15. Section 7-3 Inequalities Within a Triangle

  16. Theorem 7-6 • If the measures of three sides of a triangle are unequal, then the measures of the angles opposite those sides are unequal in the same order.

  17. Theorem 7-7 • If the measures of three angles of a triangle are unequal, then the measures of the sides opposite those angles are unequal in the same order.

  18. Theorem 7-8 • In a right triangle, the hypotenuse is the side with the greatest measure.

  19. Section 7-4 Triangle Inequality Theorem

  20. Triangle Inequality Theorem • The sum of the measures of any two sides of a triangle is greater than the measure of the third side.

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