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

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**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**

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. 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

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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. AB < JK False, because 48 is not less than or equal to 36 mLKN > mLKH True, because 45 is not greater than or equal to 90. Your Turn NK ≠ HA true mQHC < mJKH false

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

Assignment Worksheet #7-1

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Presents Section 1.3 Inequalities and Absolute Value MB1 Track This section is prepared by M. Zalzali.

Presents Section 1.3 Inequalities and Absolute Value MB1 Track This section is prepared by M. Zalzali.

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