Question

Дано: АВ=СD; ВС=DA; угол С=40 градосов.Доказать: треугольник АВD=СDВ.Найти: угол А.СРОЧНО, ПЛИЗ!!!

Answer 1

AB = CD по условию,
ВС = DA по условию,
BD - общая сторона для треугольников  АВD и СDВ, следовательно
ΔАВD = ΔСDВ по трем сторонам.

В равных треугольниках напротив равных сторон лежат равные углы:
∠А = ∠С = 40°

Answer 2

Дано: АВ = СD, ВС = DA, угол С = 40 градусов. Доказать: треугольник АВD = СDВ. Найти: угол А.

Proof:

To prove that triangle АВD is congruent to triangle СDВ, 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 congruent to the corresponding sides and angle of another triangle, then the triangles are congruent.

In this case, we are given that АВ = СD, ВС = DA, and angle С = 40 degrees. We need to show that triangle АВD is congruent to triangle СDВ.

Using the SAS criterion, we can say that: - Side AB is congruent to side CD (given: АВ = СD). - Side AD is congruent to side BC (given: ВС = DA). - Angle A is congruent to angle C (by definition of congruent angles).

Therefore, triangle АВD is congruent to triangle СDВ by the SAS criterion.

Finding angle A:

To find angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we know that angle C is 40 degrees, we can subtract this angle from 180 degrees to find the sum of angles A and B.

Let's denote angle A as x. Then, angle B can be expressed as (180 - 40 - x) degrees.

Since triangle АВD is congruent to triangle СDВ, angle B in triangle АВD is congruent to angle B in triangle СDВ. Therefore, we can equate the expressions for angle B in both triangles:

(180 - 40 - x) = (180 - 40) Simplifying the equation: -40 - x = -40 x = 0

Therefore, angle A is 0 degrees.

Conclusion:

We have shown that triangle АВD is congruent to triangle СDВ using the SAS criterion. Additionally, we have found that angle A is 0 degrees.