You write your own 2-column proof. I'll give you an outline
for it with all the reasons to put into your 2-column proof.
You use the facts that
1. the largest interior angle and side of a triangle
are opposite each other.
2. the middle side interior angle and side of a triangle
are opposite each other.
3. the smallest interior angle and side of a triangle
are opposite each other.
ΔABC is isosceles because AB≅AC, ∠B≅∠ACB because they are base angles
of isosceles ΔABC. ∠ACB is acute because the base angles of an isosceles
triangle are always acute.
∠ACD is obtuse because it is supplementary to acute ∠ACB.
∠ACD is the largest angle in ΔACD because it is obtuse.
AD is the longest side of ΔACD because it is opposite
the largest ∠ACD. AD is longer than AC, because AD is the
longest side of ΔACD. m(AD) > m(AB), because AB and AC have
the same measure. m∠B > m∠D because in ΔABD, ∠B is opposite
a longer side (AD) than the side ∠D is opposite (AB).
2. Prove that there is no regular polygon with an interior angle
whose measure is 145°.
The sum of the interior angles of a polygon with n sides is given
by the formula
Sum of interior angles = (n-2)*180°
A regular polygon of n sides has n congruent interior angles.
So each interior angle of a regular polygon has measure
.
Assume for contradiction that there exists a polygon on n sides
where n is a positive integer with an interior angle with measure
145°. Then
, where n is an integer.
Multiply both sides by n
Subtract 145°n from both sides
Add 360° to both sides
Divide both sides by 35°
That contradicts the assumption that n is a positive integer.
Therefore there is no regular polygon with an interior angle
whose measure is 145°.
Edwin