In this publication, we will consider the signs of equality of right triangles, studied in the geometry of grade 7. We will also analyze an example of solving the problem to consolidate the material presented.
Equality right triangles
Two right triangles are equal if they meet one of the following conditions.
1 sign
The leg and hypotenuse of the first right triangle are equal to the leg and hypotenuse of the second triangle.
2 sign
The two legs of the first right triangle are equal to the two legs of the second triangle.
3 sign
The leg and acute angle of the first right triangle are equal to the leg and acute angle of the second triangle.
4 sign
The hypotenuse and acute angle of the first right triangle are equal to the hypotenuse and acute angle of the second triangle.
Example of a problem
Wise trapezium ABCD, in which on the basis AD lowered two heights – BE и CF. At the same time, the segments AE и FD are equal. Prove that the trapezoid ABCD – even-handed.
Solution
Trapezium ABCD is equilateral if equal AB и CD.
Dropped to the base AD heights form two right triangles – △ABE and △FCD.
Under the conditions of the problem AE и FD, which are the legs of the considered triangles, are equal.
BE и CF are the heights of the trapezoid, which are at the same time the legs of our triangles. Like the distances between two parallel lines (the bases of a trapezoid), they also have the same length.
Thus, we have two right triangles with equal legs (AE=FD и BE=CF). This is one of the signs of equality of figures.
This means that AB = CD (hypotenuses of triangles). It follows that the trapezoid ABCD – even-handed.