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kelly ann · Jul 13, 2008, 01:25 PM

I am home-schooling and need help in presenting a two column proof of an Isosceles triangle. Need to present a two column proof for an Isosceles triangle (if the base angles of a triangle are congruent, then the triangle is Isosceles). Any help or direction to a good site would be appreciated.

galactus · Jul 13, 2008, 02:50 PM

Here are some good hints.

LEMMA:

By the SAS Postulate, $\triangle CAB\equiv\triangle CBA$

Therefore, corresponding angles $\angle CAB \;\ \text{and} \;\ \angle CBA$

are congruent. $\therefore \angle{A}\equiv\angle{B}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~

A triangle is isosceles iff the base angles are congruent.

In the light of the above, we only have to prove the converse.

If $\angle{A}\equiv\angle{B}$ ,

Then $\overline{AC}\equiv\overline{BC}$

By the ASA Theorem, $\triangle{CAB}\equiv\triangle{CBA}$

$\therefore \;\ \overline{AC}\equiv\overline{BC}$

Now, put this into a two column proof.

Here is a drawing: