whats the difference between definition of supplementary angles and congruent supplements theorem?

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Definition of supplementary angles: Two angles are called supplementary when they add to 180 degrees.

Congruent supplements theorem: supplements of congruent angles are congruent.

The congruent supplements theorem can be proven using the definition of supplementary angles, the definition of congruent angles, substitution, and the properties of equality. Many times, theorems are proven using related definitions (possibly along with other definitions, postulates, other theorems, substitution, and/or properties). Also, definitions do not need to be proven, but theorems need to be proven.

Here's a proof of the supplementary angles theorem.

Given: angle 1 is congruent to angle 2
angles 1 and 3 are supplementary
angles 2 and 4 are supplementary

Prove: angle 3 is congruent to angle 4

1) angle 1 is congruent to angle 2 1)Given
angles 1 and 3 are supplementary
angles 2 and 4 are supplementary

2) m angle 1 = m angle 2 2)Definition of congruent angles

3) m angle 1 + m angle 3 = 180 3)Definition of supplementary angles
m angle 2 + m angle 4 = 180

4) m angle 1 + m angle 3 = m angle 2 + m angle 4 4)Substitution (step 3 into step 3)

5) m angle 3 = m angle 4 5)Subtraction property of equality (steps 4 and 2)

6) angle 3 is congruent to angle 4 6)Definition of congruent angles

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Supplementary Angles Definition...Show more

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Whats the difference between definition of supplementary angles and congruent supplements theorem?
Like for proofs. I don't understand the difference.. I really need help thank you....Show more

Supplementary Definition...Show more

Supplementary angles are those that add up to 180 degrees, linear
Congruent Supplements
If two angles are supplementary to the same angle (or to congruent angles) then the two angles are congruent....Show more