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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 < b a = b a > 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. Symbol Meaning 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

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 or equal to 36 mLKN > mLKH True, because 45 is not greater than or 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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