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You are watching: What is the longest side of a triangle called

class READ-THROUGH by Dr. Carol JVF Burns (website creator) Follow together with the highlighted message while friend listen!

A 90° angle is dubbed a right angle. A ideal triangle is a triangle through a 90° angle. In a appropriate triangle, the side opposite the 90° edge is referred to as the hypotenuse and the staying two political parties are referred to as the legs. The angle in any kind of triangle include up come 180°. In any triangle, the longest side is the contrary the biggest angle, and the shortest next is the opposite the the smallest angle. Thus, in a ideal triangle, the hypotenuse is always the longest side.

The Pythagorean Theorem gives a beautiful relationship between the lengths that the political parties in a best triangle: the amount of the squares the the much shorter sides is equal to the square of the hypotenuse. Furthermore, if a triangle has actually this kind of relationship between the lengths that its sides, climate it have to be a appropriate triangle!

 THE PYTHAGOREAN THEOREM let $,,T,,$ be a triangle through sides that lengths $a$, $b$, and $c$, where $,c,$ is the longest side (if over there is a longest side). Then, $T,$ is a appropriate triangle if and only if $a^2 + b^2 = c^2,$.
have actually fun with plenty of proofs the the Pythagorean Theorem! This applet (you"ll require Java) is one of my favorites. Let that load, then keep pushing ‘Next’.
Question: intend that two angles in a triangle space 60° and also 30°. Is the a best triangle? prize YES, NO, or MAYBE.
Question: expect that a triangle has actually a 100° angle. Is the a appropriate triangle? answer YES, NO, or MAYBE.
Solution: No. The remaining two angles must sum to 80°, therefore neither continuing to be angle is a 90° angle.
Question: intend that a triangle has a 70° angle. Is that a right triangle? prize YES, NO, or MAYBE.
Solution: Maybe. The staying two angles have to sum to 110°, so among the continuing to be angles can be a 90° angle.
Question: expect the foot of a appropriate triangle have actually lengths $,3,$ and also $,x,$, and also the hypotenuse has actually length $,5,$. Uncover $,x,$.
Question: expect a triangle has sides that lengths $1,$, $sqrt3$, and $2,$. Is that a right triangle?
Solution: YES. Due to the fact that $2 > sqrt3,$, the longest side has actually length 2. And, $cssIds761^2 + (sqrt3)^2 cssIds77= 1 + 3 cssIds78= 4 cssIds79= 2^2,$.
master the concepts from this ar by practicing the practice at the bottom the this page. as soon as you"re excellent practicing, move on to: the distance Formula

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top top this exercise, you will not an essential in your answer. However, you can inspect to check out if her answer is correct. difficulty TYPES: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 accessible MASTERED IN development