Question

Докажите что ели два катета прямоугольного треугольника соответственно равны двум катетам другого прямоугольного треугольника то такие треугольники равны

Answer 1

Первый признак равенства( если две стороны и угол между ними одного треугольника равны соответственно двум сторонам и углу между ними другого треугольника, то такие треугольники равны)
т.к. 2 катета соответственно равны( по условию), то угол между ними равен тоже( по определению прямоугольного треугольника), следовательно эти треуголиники равны по первому признаку равенства 

Answer 2

Proving the Equality of Two Right-Angled Triangles' Hypotenuses

To prove that if the legs of one right-angled triangle are equal to the legs of another right-angled triangle, then the triangles are congruent, we can use the following steps:

1. Given Information: - We are given two right-angled triangles, where the legs of one triangle are equal to the legs of the other triangle.

2. Understanding the Theorem: - The theorem we are trying to prove is a part of the criteria for proving the congruence of right-angled triangles, known as the Hypotenuse-Leg (HL) congruence criterion.

3. Using the HL Congruence Criterion: - According to the HL congruence criterion, if the hypotenuse and one leg of a right-angled triangle are respectively equal to the hypotenuse and one leg of another right-angled triangle, then the triangles are congruent.

4. Applying the Criterion: - In this case, if the legs of one right-angled triangle are equal to the legs of another right-angled triangle, then the hypotenuses of the triangles are also equal. Therefore, by the HL congruence criterion, the two triangles are congruent.

5. Conclusion: - Therefore, if the legs of one right-angled triangle are equal to the legs of another right-angled triangle, then the triangles are indeed congruent.

The proof is based on the HL congruence criterion, which states that if the hypotenuse and one leg of a right-angled triangle are respectively equal to the hypotenuse and one leg of another right-angled triangle, then the triangles are congruent.