An inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (source: WIKIPEDIA). These inequalities will allow us to formulate several important geometric relationships. The types of inequalities geometry are transitive property, Substitution postulate, and trichotomy postulate. All the types of inequalities are used for proving inequality geometry.
Types of Inequalities Geometry
In geomeric inequality:
A whole is equal to the sum of all its parts. A whole is greater than any of its parts.
In geometry: The lengths of line segments and the measures of angle are positive number.
Consider these two applications:
If ACB is a line segment, then AB = AC + CB, AB > AC, and AB > CB.
If ?DEF and ?FEG are adjacent angles, m?DEG = m?DEF + m?FEG,
Types of inequalities:
Type 1: Transitive property of inequality:
if a,b, and c are real numbers such that a > b and b > c, then a > c.
Then in geometry: If BA > BD and BD > BC, then BA > BC. Also, if m?BCA > m?BCD > m?BAC, then
Type 2: Substitution postulate of inequality:
A quantity may be substituted for its equal in any statement of inequality.
In geometry: If AB . BC and BC = AC, then AB > AC. Also, if m?C > m?A and m?A = m?B, then m?C > m?B.
Type 3: The trichotomy postulate Inequality:
Given any two quantities, a and b, one and only one of the following is true;
a < b or a = b or a > b.
Proving Inequalities and its Types in Geometry
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Given: m?DAC = m?DAB + m?BAC and m?DAB > m?ABC
Prove: m?DAC > m?ABC
Statements Reasons
1. m?DAC = m?DAB + m?BAC 1. Given.
2. m?DAC > m?DAB 2. A whole is greater than any of its parts.
3. m?DAB > m?ABC 3. Given.
4. m?DAC > m?ABC 4. Transitive property of inequality.
This proof shows the inequalities geometry.
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