Question

У трецгольника АВС и А1В1С1 АВ=А1В1, АС=А1С1,<с=90. Докажите, что АВС = А1В1С1

Answer 1

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Answer 2

Given Information

We are given the following information about triangles ABC and A1B1C1: - AB = A1B1 - AC = A1C1 - ∠C = 90°

We need to prove that triangle ABC is congruent to triangle A1B1C1.

Proof

To prove that triangle ABC is congruent to triangle A1B1C1, we can use the Side-Angle-Side (SAS) congruence criterion. According to this criterion, if two triangles have two sides and the included angle of one triangle equal to the corresponding two sides and included angle of the other triangle, then the triangles are congruent.

In this case, we have: - AB = A1B1 (given) - AC = A1C1 (given) - ∠C = 90° (given)

Now, let's compare the corresponding sides and angles of triangles ABC and A1B1C1:

1. Side AB = Side A1B1 (given) 2. Side AC = Side A1C1 (given) 3. Angle ∠C = Angle ∠C (given)

Since all three conditions are satisfied, we can conclude that triangle ABC is congruent to triangle A1B1C1 by the SAS congruence criterion.

Therefore, we have proved that triangle ABC is congruent to triangle A1B1C1.

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