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7-1: Segments, Angles, and Inequalities

7-1: Segments, Angles, and Inequalities. 7-1: Segments, Angles, and Inequalities. Inequality : A statement that contain the symbol < or >. Postulate 7-1 : For any two real numbers, a and b , exactly one of the following statements is true. a < b a = b a > b.

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7-1: Segments, Angles, and Inequalities

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  1. 7-1: Segments, Angles, and Inequalities

  2. 7-1: Segments, Angles, and Inequalities • Inequality: A statement that contain the symbol < or >. • Postulate 7-1: For any two real numbers, a and b, exactly one of the following statements is true.a < ba = ba > b

  3. 7-1: Segments, Angles, and Inequalities • Example #1: Replace ? With <, >, or = to make the statement true. • SL ? RL • Remember, length can be determined by subtracting the coordinates of two points (and taking the absolute value) • 2 – (-5) ? 2 – (-3) • 7 ? 5 > • Your Turn • ND ? RD • SR ? DN < =

  4. 7-1: Segments, Angles, and Inequalities • The results from the previous example lead to the following theorem • Theorem 7-1: If point C is between points A and B, and A, B, and C are collinear, then AB > AC and AB > CB.

  5. 7-1: Segments, Angles, and Inequalities • A similar theorem can be used for comparing angles. This theorem is based on the angle addition postulate. • Theorem 7-2: If EP is between ED and EF, then mDEF > mDEP and mDEF > mPEF

  6. 7-1: Segments, Angles, and Inequalities • The graph shows the portion of music sales for each continent. Replace ? With <, >, or = to make a true statement. • mSCI ? mUCI • Because SCI is inside UCI, then by Theorem 7-2 mSCI <mUCI • Your Turn • mMCS ? mICM • mUCM ? mICM > <

  7. 7-1: Segments, Angles, and Inequalities • Inequalities comparing segment or angle measures may also include the symbols listed below.

  8. 7-1: Segments, Angles, and Inequalities • The diagram below shows plans for a garden arbor. Use the diagram to determine whether each statement is true or false. • AB < JK • False, because 48 is not less than orequal to 36 • mLKN>mLKH • True, because 45 is not greater thanor equal to 90. • Your Turn • NK ≠ HA • true • mQHC<mJKH • false

  9. 7-1: Segments, Angles, and Inequalities • Assignment • Worksheet #7-1

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