Q: Why a triangle with a two 45 degrees angles is an isosceles triangle?

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If a triangle is an isosceles triangle as well as being a right-angled triangle, the size of the two angles (that are not right angles) are 45 degrees.

An obtuse triangle or a right angle triangle. An equilateral is definitely an isoceles triangle * * * * * Not true. An obtuse or right angled triangles can be isosceles. It depends on the sizes of the two smaller angles. An isosceles triangle has two equal angles so a triangle with angles of size [A, (180-A)/2, (180-A)/2] degrees where 90 < A < 180 degrees would be an obtuse angled isosceles triangle. A triangle with angles of size (90, 45, 45) degrees is a right angled isosceles triangle.

In all triangles, the angles always measure up 180 degrees. In an isosceles triangle two of the angles are equal.

An isosceles triangle has two equal sides, and if one of the angles is 90 degrees, than the other two have to be equal. A triangle's angles always add up to 180 degrees, so the other two have to be 45 degrees.

An isosceles triangle is any triangle with at least two sides of equal length. Logically, an isosceles triangle also has at least two angles of equal size. An equilateral triangle is a triangle with three equal sides and three equal angles (all of which are 60 degrees). Since it has at least two equal sides then it is therefore also an isosceles triangle. This is no different to the way in which a square is also a rectangle, or a circle is also an ellipse. They are simply special cases of the general case.

Related questions

Isosceles Triangle. An isosceles triangle is a triangle with (at least) two equal sides/ angles.

An isosceles triangle has 3 interior angles that add up to 180 degrees, and 2 of its angles are equal and two of its sides are equal.

If a triangle is an isosceles triangle as well as being a right-angled triangle, the size of the two angles (that are not right angles) are 45 degrees.

two angles of 45 degrees

-- In any triangle, the three inside angles always add up to 180 degrees. -- In an isosceles triangle, two of the three inside angles are equal.

An obtuse triangle or a right angle triangle. An equilateral is definitely an isoceles triangle * * * * * Not true. An obtuse or right angled triangles can be isosceles. It depends on the sizes of the two smaller angles. An isosceles triangle has two equal angles so a triangle with angles of size [A, (180-A)/2, (180-A)/2] degrees where 90 < A < 180 degrees would be an obtuse angled isosceles triangle. A triangle with angles of size (90, 45, 45) degrees is a right angled isosceles triangle.

An isosceles triangle

In all triangles, the angles always measure up 180 degrees. In an isosceles triangle two of the angles are equal.

The two other angles are 45 degrees each. The three angles of every triangle always add up to 180 degrees. -- A right triangle is a triangle that has a right angle in it. -- A right angle is 90 degrees. -- That leaves 90 degrees for the other two angles in the right triangle. -- If it happens to be isosceles, then the other two angles are equal. -- Those must both be 45 degrees.

an isosceles triangle can have any vertex angle less than 180 and greater than 0, as long the other two angles are equal. an isosceles triangle with a vertex of 179 degrees would just have the other two angles be 0.5 degrees. A right triangle with matching angles (both 45 degrees) would be both a right triangle and isosceles triangle.

An isosceles triangle has two equal sides, and if one of the angles is 90 degrees, than the other two have to be equal. A triangle's angles always add up to 180 degrees, so the other two have to be 45 degrees.

An isosceles triangle is any triangle with at least two sides of equal length. Logically, an isosceles triangle also has at least two angles of equal size. An equilateral triangle is a triangle with three equal sides and three equal angles (all of which are 60 degrees). Since it has at least two equal sides then it is therefore also an isosceles triangle. This is no different to the way in which a square is also a rectangle, or a circle is also an ellipse. They are simply special cases of the general case.