They aren't necessarily similar to each other. There are many different kinds of isosceles triangle. There is only one kind of equilateral triangle, though they come in different sizes, so all equilateral triangles are similar to each other. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. Two isosceles right triangles can have different side lengths, and they will still be isosceles right. Both of the triangles are right angled, and the hypotenuse and another side of one are the same length as the hypotenuse and another side of the other. No, not all isosceles right triangles are congruent.

Erecting similar isosceles triangles on the edges of an initial triangle.

Two of the angles of one and the side between those two angles equal the corresponding angles and side of the other (ASA). If these isosceles triangles are similar, then they must follow either one of the AA or SAS criterion but they cannot because none of the angles is equal to one another. Another special case of an isosceles triangle is the isosceles right triangle.

Two of the sides of one and the angle between those two sides equal the corresponding sides and angle of the other (SAS).

The sides of one are all equal in length to the sides of the other (SSS).

There are four tests that can be used to prove that two triangles are congruent: In the following we use 'S' as an abbreviation for Side, and A as an abbreviation for Angle, so (Side-Side-Side) is written as (SSS). It is a special isosceles triangle with one angle being a right angle and the other two angles are congruent as the angles are opposite to the equal sides. There is only one triangle that can be made with sides of length 6 cm, 7cm and 8 cm. That's because, for example, once you know the lengths of the three sides of a triangle the angles are completely determined.

Knowing that triangle ABC is isosceles simplifies the similarity. (ii) Two isosceles-right triangles are similar. that the right triangle is isosceles but the same argument can be applied in general.

When we want to prove that two triangles are congruent, we don't need to prove all six correspondences. State, true or false: (i)All isosceles triangles are similar. When two triangles are congruent, the angles of one triangle are the same as the angles of the other and the lengths of the sides of one triangle are the same as the lengths of the sides of the other.

Right isosceles triangles are similar