Title: Lesson 33: Inequalities and Geometric Inequalities
1Lesson 33 Inequalities and Geometric Inequalities
2Homework
- Will unequals multiplying/dividing unequals
produce inequality in the same order or produce
equality? Can you give any examples to support
your conclusions? - Geometry, P206-207, 6-13
3Do Now What is inequality and what are the basic
inequality postulates?
- Definition of Greater Than
- Trichotomy Postulate of Inequality
- Transitive Postulate of Inequality
- Addition Postulate of Inequality
- Subtraction Postulate of Inequality
- Multiplication Postulate of Inequality
- Division Postulate of Inequality
- Substitution Postulate of Inequality
41. Definition of Greater Than
- Suppose a and b are real numbers. agtb if and only
if there is a positive real number c such that a
bc. Also, blta is equivalent to agtb. - Examples real numbers, segments, angles
5Example1 How do we use basic inequality
postulates to prove geometric inequality
relationships?
- Prove that the measure of an exterior angle of a
triangle is greater than the measure of either
remote interior angles. (Theorem 6-1)
62. Trichotomy Postulate
- Suppose a and b are real numbers. Either agtb,
altb, or ab.
73. Transitive Postulate of Inequality
- Suppose a, b and c are real numbers. If agtb and
bgtc, then agtc.
8Example 2 How do we use basic inequality
postulates to prove geometric inequality
relationship?
- Given In ?ABC, ABgtAC and M is the midpoint
of segment AC. - Prove ABgtAM
94. Addition Postulate of Inequality
- Suppose a, b, c and d are real numbers.
- If agtb, then acgtbc
- If agtb and cgtd, then acgtbd
105. Subtraction Postulate of Inequality
- Suppose a, b, and c are real numbers. If agtb,
then a-cgtb-c. - Q What happens when unequals are subtracted from
unequals?
11Example 3 How do we use basic inequality
postulates to prove geometric inequality
relationship?
- Given m?ABCltm?EFG. D and H are points inside
?ABC and ?EFG respectively. ?DBC??HFC - Prove ?ABDlt?EFH
126. Multiplication Postulate of Inequality
- Suppose a, b and c are real numbers.
- If agtb and cgt0, then acgtbc.
- If agtb and clt0, then acltbc.
- Q Will unequals multiplying/dividing unequals
produce inequality in the same order or produce
equality? Can you give any examples to support
your conclusions? (Homework)
137. Division Postulate of Inequality
- Suppose a, b and c are real numbers.
- If agtb and cgt0, then a/cgtb/c.
- If agtb and clt0, then a/cltb/c.
- Q Will unequals multiplying/dividing unequals
produce inequality in the same order or produce
equality? Can you give any examples to support
your conclusions? (Homework)
148. Substitution Postulate of Inequality
- Suppose a, b and c are real numbers. If agtb and
ac, then cgtb.
15Example 4 How do we use basic inequality
postulates to prove geometric inequality
relationship?
- Given ABltCD. X and Y are the midpoints of
segments AB and CD respectively. - Prove AXltCY