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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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2.6 Algebraic Proof. Objectives Use algebra to write two-column proofs Use algebra to write two-column proofs Use properties of equality in geometry proofs.

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