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: