Chapter 6 Review

+DEFINITION OF INEQUALITY

Difference in size, degree or congruence

AB

∠A <∠B20 70

+ADDITION POI

IF and a >b c≥dTHEN

a +c>b+dEXAMPLE:

IF and 5 > 2 10≥7THEN

5 +10 > 2 + 715 > 9

+Multiplication POI

IF and a >b c > 0THEN

ac >bcEXAMPLE:

IF and 5 > 2 10 > 0THEN

5 • 10 > 2 • 1050 > 20

+Multiplication POI

IF and a >b c < 0THEN

ac <bcEXAMPLE:

IF and 5 > 2 −10 < 0THEN

5 • −10 < 2 • −10−50 < −20

+DIVISION POI

IF and a >b c > 0THEN

a

c>

bc

EXAMPLE:

IF and 20 >15 5 > 0THEN

20

5>

155

= 4 > 3

+DIVISION POI

IF and a >b c < 0THEN

a

c<

bc

EXAMPLE:

IF and 20 >15 −5 < 0THEN

20

−5<

15−5

= −4 < −3

+Transitive POI

IF and a >b b > cTHEN

a > cEXAMPLE:

IF and 5 > 2 2 >1THEN

5 >1

+POI

IF and a=b+c c > 0THEN

a >bEXAMPLE:

IF and 10=2+8 8 > 0THEN

10 > 8

+Exterior angle inequality theorem

The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

∠4 >∠1and

∠4 >∠21

2

4

+Indirect Proofs

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction of a known fact.

3. State that the temporary conclusion is false.

4. Therefore the original conclusion must be true.

THEOREM: If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.What you need to understand: The angle opposite the longest side in a triangle is the largest angle.

12

10

4

CA

B <B is opposite the largest side.Therefore, <B is the largest angle.

Conversely, the largest side is across from the largest angle.

85

30

65CA

B AC is the longest side.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

SAS Inequality Theorem

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

SSS Inequality Theorem

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.

HOMEWORK

PG 6301-12 all

PG 6311-11 (omit 4, 5 and 8)

Worksheets (green and blue)