If two angles are supplementary to the same angle, then
they are congruent to each other
they are congruent to each other.
Supplementary angles are two angles that add up to 180 degrees. To prove that two angles are congruent, we need to show that they have the same measure.
Let’s suppose that angle A and angle B are both supplementary to angle C.
We know that angle A + angle C = 180 degrees and angle B + angle C = 180 degrees.
Now we can set up an equation to find the relationship between angle A and angle B.
angle A + angle C = angle B + angle C
By subtracting angle C from both sides of the equation, we get:
angle A = angle B
This shows that angle A and angle B have the same measure and therefore are congruent to each other.
So, if two angles are supplementary to the same angle, they are congruent to each other.
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