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Can a triangle be a right triangle if all sides are congruent? - Answers

No. If all sides of a triangle are congruent then so are the angles. And, since the three angles sum to 180 degrees, each angle MUST be 60 degrees. So there cannot be any right angle in such a triangle. Another way to look at it is, according to the Pythagoras theorem, the square on the hypotenuse is equal to the sum of the squares on the two legs of a right angled triangle. But in this case, the three are congruent (each of length x units), so x2 = x2 + x2 or x2 = 2x2 which can only be true if x = 0 or if 1 = 2 The first option gives a triangle whose sides have no length! while the second states that 1 = 2. Neither is possible and hence you cannot have such a triangle.



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Can a triangle be a right triangle if all sides are congruent? - Answers

https://math.answers.com/math-and-arithmetic/Can_a_triangle_be_a_right_triangle_if_all_sides_are_congruent

No. If all sides of a triangle are congruent then so are the angles. And, since the three angles sum to 180 degrees, each angle MUST be 60 degrees. So there cannot be any right angle in such a triangle. Another way to look at it is, according to the Pythagoras theorem, the square on the hypotenuse is equal to the sum of the squares on the two legs of a right angled triangle. But in this case, the three are congruent (each of length x units), so x2 = x2 + x2 or x2 = 2x2 which can only be true if x = 0 or if 1 = 2 The first option gives a triangle whose sides have no length! while the second states that 1 = 2. Neither is possible and hence you cannot have such a triangle.



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https://math.answers.com/math-and-arithmetic/Can_a_triangle_be_a_right_triangle_if_all_sides_are_congruent

Can a triangle be a right triangle if all sides are congruent? - Answers

No. If all sides of a triangle are congruent then so are the angles. And, since the three angles sum to 180 degrees, each angle MUST be 60 degrees. So there cannot be any right angle in such a triangle. Another way to look at it is, according to the Pythagoras theorem, the square on the hypotenuse is equal to the sum of the squares on the two legs of a right angled triangle. But in this case, the three are congruent (each of length x units), so x2 = x2 + x2 or x2 = 2x2 which can only be true if x = 0 or if 1 = 2 The first option gives a triangle whose sides have no length! while the second states that 1 = 2. Neither is possible and hence you cannot have such a triangle.

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      No. If all sides of a triangle are congruent then so are the angles. And, since the three angles sum to 180 degrees, each angle MUST be 60 degrees. So there cannot be any right angle in such a triangle. Another way to look at it is, according to the Pythagoras theorem, the square on the hypotenuse is equal to the sum of the squares on the two legs of a right angled triangle. But in this case, the three are congruent (each of length x units), so x2 = x2 + x2 or x2 = 2x2 which can only be true if x = 0 or if 1 = 2 The first option gives a triangle whose sides have no length! while the second states that 1 = 2. Neither is possible and hence you cannot have such a triangle.

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