True or False? A right triangle with two congruent legs is always a 45-45-90 triangle.
2007-01-04 10:20:12 · 11 answers · asked by JoAnna 2 in Science & Mathematics ➔ Mathematics
True, but I'm not sure how to prove it.
2007-01-04 10:24:32 · answer #1 · answered by sgasner 2 · 0⤊ 1⤋
This is true.
The longest side will be the hypotenuse. The legs, being congruent mean that the opposite angles (not the right angle) will be equal. Since the angles add up to 180, that means you have x + x + 90 = 180.
2x + 90 = 180
2x = 90
x = 45
Therefore you must have a 45-45-90 triangle.
2007-01-04 10:31:48 · answer #2 · answered by Puzzling 7 · 1⤊ 0⤋
This is true. In a right triangle,
a^2 + b^2 = c^2 where c is the leg across from the right angle. This also means that c is longer than sides a and b. Since two sides are congruent, can c cannot be one of them, then a and b must be equal. If the sides are equal, there angles will also be equal, hence you have a 45,45,90 triangle.
2007-01-04 10:34:19 · answer #3 · answered by Anonymous · 0⤊ 0⤋
true. 180 degrees in a triangle. the only way to make an 2 equal angles and one other is a 45 45 90.
2007-01-04 10:26:45 · answer #4 · answered by travis R 4 · 1⤊ 0⤋
True. What you are referring to is actually an isosceles triangle. An isosceles triangle has two congruent legs and a third side called the base. Since you are also describing a right triangle, the "base" is the hypoteneuse.
The angle in between the congruent legs is called the vertex angle, and in this case is 90º. The other two angles are called base angles. By definition of an isosceles triangle, the base angles are always congruent. Since your vertex angle is 90º, the base angles must add up to 90º. Since the base angles are congruent, they must both be 45º.
Hope this helps!
2007-01-04 10:32:21 · answer #5 · answered by lil e 2 · 0⤊ 0⤋
true...if you imagine that you have 3 noodles and want to make a triangle...2 of them being the same size...if you connect them all to make a triangle then you will always have a 90 deg. angle and always 2, 45 deg. angles...its just the way it works
2007-01-04 10:54:17 · answer #6 · answered by Anonymous · 0⤊ 0⤋
the respond is 'genuine'. extremely some human beings have stated that it may additionally be equilateral, yet this would not end it from being isosceles, it in uncomplicated terms makes it a different form of isosceles triangle.
2016-10-06 10:55:06 · answer #7 · answered by ? 4 · 0⤊ 0⤋
I dont know
2007-01-04 10:22:13 · answer #8 · answered by qwerty 2 · 0⤊ 0⤋
True!!!
2007-01-04 11:10:53 · answer #9 · answered by Anonymous · 0⤊ 0⤋
Unless it is equilateral.
2007-01-04 10:26:23 · answer #10 · answered by Earnesty_in_life 3 · 0⤊ 1⤋