What is the flaw in the proof that all triangles are isosceles?

The problem is that the perpendicular and the bisector do not intersect inside the triangle, as the picture erroneously suggests. In fact, this fallacy is a proof by contradiction that for non-isosceles triangles the intersection point P is necessarily outside of the triangle.

What theorem prove a triangle is isosceles?

If a triangle has two congruent angles, then the sides opposite those angles are congruent. In other words, iso-angular triangles are iso-lateral (isosceles). This is the converse of the isosceles triangle theorem.

Is every triangle an isosceles triangle?

Every triangle is isosceles.

What’s true for all triangles?

Properties of a triangle A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side.

Is all triangles are similar?

All equilateral triangle are similar. It cannot be isosceles as for being similar triangle, the corresponding angle must be same and length of sides are in same ratio. In case of equilateral triangle, angles are always same and sides are in the same ratio, whereas it is not in case of isosceles triangle.

How do you prove that a triangle is isosceles in a circle?

We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches. We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.

Which of the following triangles are isosceles triangle?

The two equal sides are called the legs and the third side is called the base of the triangle….