The relationship between waist and base of isosceles right triangle: waist is equal to twice of 1/2 bases; The included angle between the waist height and the bottom edge is equal to half of the top angle; The distance between the middle vertical line on the bottom edge and the two waists is equal. An isosceles right triangle is a special kind of triangle, which has all the properties of a triangle: stability, two right angles are equal, the right angle forms an acute angle of 45, the vertical lines of the bisector of the median angle on the hypotenuse are combined, and the height on the hypotenuse of the isosceles right triangle is the radius r of the circumscribed circle, so if the radius r of the inscribed circle is 1, the radius r of the circumscribed circle is √ 2+/kloc-0. An isosceles right triangle is a special isosceles triangle (one angle is a right angle) and a special right triangle (two right angles, etc.). ), so the isosceles right triangle has all the properties of isosceles triangle and right triangle (such as the unity of three lines, pythagorean theorem, hypotenuse midline theorem of right triangle, etc. ). Of course, isosceles right-angled triangles also have the properties of general triangles, such as sine theorem, cosine theorem, angle bisector theorem, midline theorem and so on. The ratio of three sides of an isosceles right triangle is.

The relationship between the waist and the bottom of an isosceles triangle is: the bottom =√(2* the square of the waist length) =(√2)* the waist length.

An isosceles right triangle is a special kind of triangle, which has all the properties of a triangle: stability, two right angles are equal, the right angles have an acute angle of 45, and the perpendicular of the median bisector on the hypotenuse is an integral.

The height on the hypotenuse of an isosceles right triangle is the radius r of the circumscribed circle, so let the radius r of the inscribed circle be 1 and the radius r of the circumscribed circle be √2+ 1, so r/r =1(√ 2+1).

Extended data:

The isosceles right triangle is a special isosceles triangle, which is characterized by:

1, and the two base angles are equal to 45.

2, the two waists are equal.

3. The ratio of three sides of an isosceles right triangle is 1: 1: √ 2.

Determination of isosceles triangle;

1, an isosceles triangle with a right angle, or a right triangle with two equal sides is an isosceles right triangle.

2. A triangle with the ratio of three sides 1: 1: √ 2 is an isosceles right triangle.

3. An isosceles triangle with a base angle of 45 is an isosceles right triangle.

4. A right triangle with an acute angle of 45 is an isosceles right triangle.

5. The right triangle with the ratio of right angle to hypotenuse 1: √ 2 is an isosceles right triangle.

6. A triangle with an angle of 45, the length ratio of the opposite side of this angle to its side is 1: √ 2 is an isosceles right triangle.