Isosceles Triangles
A triangle is said to be isosceles if
- Two sides in it have equal length, or
- Two angles in it are equal.
The next two theorems show that the conditions (1) and (2) are
equivalent. That is, each implies the other.
Digression: To encourage further site
exploration, here are two site
descriptions
- Math Forum, 1996 online classification of the
then dozen or so math lesson giving websites: ...
There are appetizers for algebra,
arithmetic,
logic,
better
learning in general, reason,
theorem
proving and complex
numbers. Strengths here are in Alan's explanation of
mathematical concepts using words
and stories:
...
- Magellan, the McKinley Internet Directory, 1996:
Mathphobics, this site may ease your fears of the subject, perhaps
even help you enjoy it. The tone of the little lessons and
"appetizers" on math
and logic
is unintimidating, sometimes funny and very clear. There are a
number of different angles offered, and you do not need to follow
any linear lesson plan. Just pick and peck. The site also offers
some reflections
on teaching, so that teachers can not only use the site as part
of their lesson, but also learn from it.
Where there is smoke, there is fire. Bon Appetite.
Theorem 1. If two sides in a triangle have equal lengths
then the angles opposite them are equal.
Proof of theorem 1:
Click on thumbnail to see proof.
Theorem 2. If two angles in a triangle are equal then the sides
opposite them have equal length.
Proof of theorem 2:
Click on thumbnail to see proof.
Equilateral and Equiangular Triangles
A triangle is said to be equilateral when and only when all
three sides in it have the same length. A triangle is said to be equiangular
when and only when all three angles in it are equal.
Theorems 1 and 2 above imply the following.
Theorem 3. A triangle is equilateral when and only when it is
equiangular.
|