The Statement vs. Reason chart normally used for proofs in high schools across the USA is a common thing.
"An exterior angle of a triangle is greater than either remote interior angle."
Can I prove this corollary using numbers instead of the statement vs reasons chart?
Let angle A = exterior angle
Let BCD = a triangle
Let angle B = 70 degrees
Let angle C = 10 degrees
Let angle D = 100 degrees
Then angles A and angle D form a linear pair on a straight line.
Then the measure angle A = 180 degrees - the measure of angle D, which is 100 degrees. The number 180 comes from the fact that a straight line measures 180 degrees.
Of course, 180 - 100 = 80.
So, the measure of angle A = 80 degrees, which is indeed GREATER THAN than EITHER of the two remote interior angles of 10 degrees and 70 degress.
Can this accepted as the prove for the above corollary without using the statement vs reasons chart that often confuses students far and near?
Also, can this method with numbers be used for any geometric proofs situation?
Masters is right. The way I would prove this statement is to show that an exterior angle of a triangle is equal to the sum of the two remote interior angles. Since no angle can be equal to zero, neither of the two remote interior angles will be as large as the exterior angle.
Reasons are in red.
1) Angles 1 and 2 make up a linear pair which total 180 degrees.
2) The sum of the measures of the angles of a triangle = 180 degrees.
3) Subtraction using Step 1.
4) Subtraction using Step 2.
5) Substitution, using Steps 3 and 4.
6) A sum is greater than each of its parts.