Inequalities

Question 1

Add Prop >

Answer 1

if a > b, c >d then a + c > b + d

Question 2

Mult Prop >

Answer 2

if a > b, c > 0 then ac > bc if a > b, c < 0 then ac < bc

Question 3

Trans Prop >

Answer 3

if a > b, b >c then a > c

Question 4

Whole > Part Prop ≠

Answer 4

if a = b + c, b > 0 a > c

Question 5

Prop ≠

Answer 5

if a + c = b + d, a > b then c < d

Question 6

Substitution

Answer 6

if a > b, b = c then a > c

Question 7

Exterior Angle Inequality Theorem

Answer 7

An exterior angle of a triangle is greater than each remote interior angle

Question 8

Triangle Inequality Theorem

Answer 8

Two sides of a triangle have a sum greater than the third side

Question 9

Larger Side –> Larger Angle (LS LA)

Answer 9

The larger side of a triangle is opposite the larger angle - comparison in one triangle

Question 10

SAS ≠ Theorem (Hinge Theorem)

Answer 10

If two sides are congruent and their included angles are unequal, the triangle with the larger angle has the larger side (smaller angle –> smaller side)

Question 11

SSS ≠ Theorem (Converse Hinge Theorem)

Answer 11

If two sides are congruent and the third sides are unequal, the triangle with the larger side has the larger angle (smaller side —> smaller angle)

Question 12

Converse Pythag Theorem

Answer 12

(c represents the length of the longest side) c²= a² + b² angle C is right

c² > a² + b² angle C is obtuse

c² < a² + b² angle C is acute