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

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

<=

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.

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

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

><

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

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

mLKN > mLKH True, because 45 is not greater than

or equal to 90.Your Turn

NK ≠ HA true

mQHC < mJKH false

7-1: Segments, Angles, and Inequalities

Assignment Worksheet #7-1