Posted by Jeffrey on .
I'm stuck on these 2 problems. My Geometry teacher won't help me.
What is the inverse of the Isosceles Triangle Theorem (ITT)?
What is the contrapositive of the Isosceles Triangle Theorem (ITT)?

Honors Geometry 
Damon,
Here is how I remember this:
1. hypothesis
If a cow, then a mammal.
assume true
2. converse
If a mammal, then a cow.
maybe
3. inverse
If not a cow, then not a mammal.
maybe
4. contrapositive
If not a mammal, then not a cow.
true
You can also draw Venn diagram to remember this. 
Honors Geometry 
Damon,
So
I am not sure how your book stated theorem, there are several "isosceles triangle theorems.
here is perhaps the most likely:
Hypothesis:
If two sides equal, then opposite angles equal.
Inverse
If two sides not equal, then opposite angles not equal
Contrapositive
If two angles not equal, then opposite sides not equal. 
Honors Geometry 
Jeffrey,
hmm.. okay, but i'm not really seeing how that goes with the ITT

Honors Geometry 
Damon,
Tell me what ITT is exactly.

Honors Geometry 
Damon,
Put your ITT in the form
IF THIS
THEN THAT
That is the hypothesis. The rest just follows the recipe. 
Honors Geometry 
Jeffrey,
Okay, the ITT is
If a triangle has two congruent sides, then the angles oppositeof those sides are congruent 
Honors Geometry 
Jeffrey,
Okay. I figured the problem out now. Thanks for your help!

Honors Geometry 
Damon,
Good, I figured you would !