Posted by **Jeffrey** on Friday, January 18, 2008 at 10:48am.

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**, Friday, January 18, 2008 at 10:55am
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**, Friday, January 18, 2008 at 11:07am
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**, Friday, January 18, 2008 at 11:10am
hmm.. okay, but i'm not really seeing how that goes with the ITT

- Honors Geometry -
**Damon**, Friday, January 18, 2008 at 11:16am
Tell me what ITT is exactly.

- Honors Geometry -
**Damon**, Friday, January 18, 2008 at 11:18am
Put your ITT in the form

IF THIS

THEN THAT

That is the hypothesis. The rest just follows the recipe.

- Honors Geometry -
**Jeffrey**, Friday, January 18, 2008 at 11:25am
Okay, the ITT is

If a triangle has two congruent sides, then the angles oppositeof those sides are congruent

- Honors Geometry -
**Jeffrey**, Friday, January 18, 2008 at 1:49pm
Okay. I figured the problem out now. Thanks for your help!

- Honors Geometry -
**Damon**, Friday, January 18, 2008 at 3:54pm
Good, I figured you would !

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