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Given any triangle ABC, a+b__c, a+c__b, and b+c__a

greater

The sum of any 2 sides of a triangle is ... than the 3rd side

longest side

potential hypotenuse =

a squared + b squared = c squared, C

If ..., then triangle ABC is right with hypotenuse...

a squared plus b squared > c squared

If ..., then triangle ABC is acute

a squared plus b squared < c squared, C

If..., then triangle ABC is obtuse with obtuse angle ...

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inverse ITT: If 2 sides of one triangle are side a < side b, then angle A ... angle B

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inverse CITT: If two angles of one triangle are angle D < angle F, then side d ... side f

hinge theorem

HT (aka SAS inequality)

converse hinge theorem

CHT (aka SSS inequality)

sum

the external angle is the ... of the two remote interior angles

difference, sum

when determining the restrictions of a side of a triangle, the smaller number is the ... between the 2 other sides and the larger restriction is the ... of the 2 other sides

smaller

Hinge Theorem: if the 2 other corresponding sides are congruent and the opposite angle is smaller than the opposite angle of the other triangle, then the angle is ... than the angle in the other triangle

larger

converse hinge theorem: if the 2 other corresponding sides are congruent and the opposite angle is larger than the opposite angle of the other triangle, then the angle is ... than the angle in the other triangle