Honors Geometry

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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 -

    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 -

    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 -

    hmm.. okay, but i'm not really seeing how that goes with the ITT

  • Honors Geometry -

    Tell me what ITT is exactly.

  • Honors Geometry -

    Put your ITT in the form

    IF THIS

    THEN THAT

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

  • Honors Geometry -

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

  • Honors Geometry -

    Okay. I figured the problem out now. Thanks for your help!

  • Honors Geometry -

    Good, I figured you would !

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