A right triangle is a geometric figure with a right angle. There are two kinds of right-angled triangles: ordinary right-angled triangles and isosceles right-angled triangles. It conforms to Pythagorean theorem and has some special properties and judgment methods.

Right-angled triangles are shown in the figure: there are two cases, namely, ordinary right-angled triangles and isosceles right-angled triangles (special cases). In a right triangle, the two sides adjacent to the right angle are called right angles, and the side opposite to the right angle is called hypotenuse. The right angle of a right triangle is also called a "chord". If the lengths of two right-angled sides are not equal, the short side is called "hook" and the long side is called "strand".

An isosceles right triangle is a special triangle, which has all the properties of a triangle: stability, and the sum of internal angles is 180. The two right angles are equal and the two acute angles are 45 degrees. The vertical lines on the midline, bisector and hypotenuse are unified, and the height on the hypotenuse of an isosceles right triangle is the radius r of the circumscribed circle of the triangle, which is half of the hypotenuse.

In addition to the properties of the general triangle, it also has some special properties:

1, the sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse. As shown in figure ∠ BAC = 90, then AB? +AC？ =BC？ (Pythagorean theorem)

2. In a right triangle, two acute angles are complementary. As shown in the figure, if ∠ BAC = 90, ∠ B+∠ C = 90.

3. In a right triangle, the median line on the hypotenuse is equal to half of the hypotenuse (that is, the outer center of the right triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle R=C/2). This property is called the hypotenuse midline theorem of right triangle.

4. The product of two right angles of a right triangle is equal to the product of hypotenuse and hypotenuse height.

5. As shown in the figure, in Rt△ABC, ∠ BAC = 90, and AD is the height on the hypotenuse BC, then the projective theorem is as follows:

( 1)(AD)？ =BD DC .

(2) (AB)? =BD BC .

(3) (AC)? =CD BC .

Projection theorem, also known as Euclid theorem: in a right triangle, the height on the hypotenuse is the median of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the ratio of the median of the projection of this right-angled side on the hypotenuse to the hypotenuse. It is an important theorem of mathematical graphic calculation.

6. In a right triangle, if there is an acute angle equal to 30, then the right side it faces is equal to half of the hypotenuse.

In a right triangle, if there is a right-angled side equal to half of the hypotenuse, then the acute angle of this right-angled side is equal to 30.

I hope it can help you solve the problem.