Upload
christian-glenn
View
214
Download
0
Tags:
Embed Size (px)
Citation preview
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