Geometry  Triangle Inequalities  Chapt. 6
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Transitive:
If a < b and b < c then __a < c______

Transitive:
If a > b and b > c then __a > c___

Substitution:
If a > b and b = c then ____a > c____

Addition and Subtraction:
Inequality ___does NOT___ change when adding and subtracting.
If a > b then a + c > b + c
Add ≠

Multiplication and Division:
** If c > 0
Inequality __does NOT___ change when multiplying or dividing by positive number
If a > b then 3a > 3b
Multiplication ≠

Multiplication and Division:
** If c < 0
Inequality __does____ change when multiplying and dividing by negative number
If a > b then <

Whole is always __greater than__ either part!

Define:
Exterior Angle ≠ Theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

Exterior < ≠ Theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
m
< BCD > m < A
m
< BCD > m < B

Exterior < ≠ Theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
m < 4 > m < 1
m < 4 > m < 2

If one side of triangle is greater than another side, then the measure of the angle opposite the __big___ side is __greater__ than the measure of the angle opposite the _small__ side.

If the measure of one angle of a triangle is greater than the measure of another angle of the triangle, then the side ____opposite___ the bigger angle is ___bigger___ than the side opposite the smaller angle.

List the angles and sides in order from least to greatest.

Define:
Triangle Inequality Theorem
The sum of the lengths of any two sides of triangle must be greater than the length of the third side.


The perpendicular segment form a point to a line is the shortest segment from the point to the line

Which side of the triangle above is the smallest?
In order to find out which side of the triangle is the smallest, we must first sure out which angle of the triangle is the smallest (because the smallest side will be the opposite the smallest angle). We must use the
Triangle Angle Sum Theorem to figure out the measure of the missing angle.
 m < D + m < E + m < V = 180
 48 + 87 + m < V = 180
 135 + m < V = 180
 m < V = 45

SAS ≠
If two sides are congruent to another triangle and the included angle in the first is larger than the opposite triangle's one, then the side is longer than the other side

SSS ≠
If two sides are congruent to the other triangle, then the angle is greater than the other angle