# Geometry (Proof right triangle angle sum is 180)

## Main Question or Discussion Point

Hi guys not sure were this goes sorry...

It's been a while sense I have taken geometry so my skills are a little rusty...

It tunrs out that I need to prove that the angles in a right tranlge add up to 180

I have looked on the internet and people just tell me oh this angle and that angle are complementary

However this does me no good as I no longer know how to prove that two angles are complementary I do remeber what it means just don't remeber how to prove it...

so if you could point me to a proof for right triangles that the sum of all of its angles is 180 that would be great

please tell me in statement reason format because just telling me two angles are complementary wont tell me anything becasue I don't remeber how to prove why two angles are complementary but I still remeber what it means...

Thanks guys!!!

HallsofIvy
Homework Helper
Why prove that a right triangle's angles add to 180 degrees? That is true in any triangle (in Euclidean geometry) and depends upon properties of parallel lines (which is why I added "in Euclidean geometry"). At one vertex, construct a line parallel to the side of the triangle opposite that vertex. Now show that the three angles the triangle makes with that line are congruent to the three angles in the triangle (one of them is an angle in the triangle, the other two are "alternating interior angles").

Is this any help? The five steps on the right support the main proof (6) on the left. Pairs of lines with double dashes through them are parallel to each other. Pairs of lines with single dashes through them are also parallel to each other. Like Halls of Ivy says, the angles of any triangle (in Euclidean space) add up to 180 degrees, not just a right-angled triangle. I drew an acute triangle, but the same logic applies to right-angled or obtuse triangles. The technical term for a pair of angles which add up to 180 degrees is "supplementary".

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• Cozma Alex
I think it is better to think of the angles of a triangle adding up to a straight angle, or half a circle. The the notion of degrees is a purely arbitrary add on, but this may not be clear to the student.

Euclid, Book 1, Proposition 32 says the sum of the three interior angles of a triangle add up to two right angles.