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7-1: Segments, Angles, and Inequalities

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I NEQUALITY : A statement that contain the symbol. Postulate 7-1: For any two real numbers, a and b, exactly one of the following statements is true. a b

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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 < =

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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.

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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 mDEF > mDEP and mDEF > mPEF

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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. mSCI ? mUCI Because SCI is inside UCI, then by Theorem 7-2 mSCI < mUCI Your Turn mMCS ? mICM mUCM ? mICM > <

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7-1: Segments, Angles, and Inequalities Inequalities comparing segment or angle measures may also include the symbols listed below. SymbolMeaning ≠is not equal to ≤less than or equal to ≥greater than or equal to ≤is not less than or equal to ≥is not greater than or equal to

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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. AAB < JK FFalse, because 48 is not less than or equal to 36 mm LKN > m LKH TTrue, because 45 is not greater than or equal to 90. Your Turn NNK ≠ HA ttrue mm QHC < m JKH ffalse

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Assignment Worksheet #7-1

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