Question

Дано: BM перпендикулярен АC; AM=MC Докозать: треугольник АВМ= треугольник СВМ​

Answer 1

Рассмотрим треуг. ABM и треуг. CBM

1)BM-общая

2)АМ=МС(по условию)

Значит треуг. АВМ= треуг.СВМ по двум катетам

Answer 2

Given Information:

We are given that BM is perpendicular to AC and that AM is equal to MC.

To Prove:

We need to prove that triangle ABM is congruent to triangle CBM.

Proof:

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

In this case, we can see that: - Side AB is equal to side CB (both are equal to BM). - Side AM is equal to side CM (given). - Angle BAM is equal to angle CBM (both are right angles, as BM is perpendicular to AC).

Therefore, we have the following congruence: - Side AB = Side CB - Side AM = Side CM - Angle BAM = Angle CBM

By the SAS congruence criterion, we can conclude that triangle ABM is congruent to triangle CBM.

Conclusion:

We have proven that triangle ABM is congruent to triangle CBM using the Side-Angle-Side (SAS) congruence criterion.