Question

Доказательство первого признака равенства треугольников. P.S в Интернете полно доказательств, но там везде "При наложении друг на друга", а такое нельзя.Рисунок, если можно.Спасибо!

Answer 1

Первый признак равенства треугольников:СУС (сторона,угол,сторона)
Если две стороны и угол между ними одного треугольника соответственно равны двум сторонам и углу между ними другого треугольника, то эти треугольники равны.

Answer 2

Proof of the First Property of Triangle Congruence

The first property of triangle congruence states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

To prove this, we can use the following steps:

1. Given: Two triangles ABC and DEF, where side AB is equal to side DE, side BC is equal to side EF, and angle A is equal to angle D. 2. To prove: Triangle ABC is congruent to triangle DEF.

Proof Steps:

1. Draw the given triangles ABC and DEF. 2. Mark the given equal sides and angles. 3. By the given information, side AB is equal to side DE, side BC is equal to side EF, and angle A is equal to angle D. 4. Now, we can superimpose triangle DEF on triangle ABC such that side DE coincides with side AB and side EF coincides with side BC. 5. Since the sides and angles of the two triangles coincide, we can conclude that triangle ABC is congruent to triangle DEF.

This visual representation demonstrates that the two triangles are congruent based on the given information.

I hope this explanation helps! If you have any further questions or need additional clarification, feel free to ask.