Question 253145: please explain why its possible to have an isosceles right triangle but not an equilateral right triangle
Found 3 solutions by jim_thompson5910, edjones, rapaljer:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! An equilateral triangle is a triangle with sides of equal length. This means that the angles are of the same measure. Since there are 3 angles, and they add up to 180 degrees, this means that each angle is 60 degrees (since 60+60+60=3*60=180 degrees). Since each angle is 60 degrees, none of these angles are 90 degrees, which is a requirement to be a right triangle.
On the other hand, it is very possible to have an isosceles triangle that is also a right triangle. Just draw a triangle with two equal sides and a right angle.
Answer by edjones(8007)  (Show Source):
You can put this solution on YOUR website! An equilateral right triangle would have three 90 degree angles. The sum of the angles of a triangle is always 180 degrees.
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Ed
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! Isosceles means two sides and therefore two angles are equal. You could have a right triangle that is 90 degrees, 45 degrees, and 45 degrees.
However, if the triangle is equilateral, this means that ALL three sides and therefore ALL three angles are equal. If all three angles are equal and total 180 degrees, they all have to be 60 degrees. This is NOT a right triangle.
Dr. Robert J. Rapalje, Retired
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