Question

Решите , плз В четырехугольнике АВСД ВС=АД и ВС//АД. Докажите, что треугольник АВС равен треугольнику СДА. С чертежом, прошу вас!!! Очень нужно

Answer 1

По 3 признаку равенства треугольников

Answer 2

Problem Statement

You have given a quadrilateral ABCD, where VS = AD and VS is parallel to AD. You need to prove that triangle ABC is congruent to triangle SDA.

Solution

To prove that triangle ABC is congruent to triangle SDA, 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 are given that VS = AD and VS is parallel to AD. Let's label the points as follows: - A: vertex of triangle ABC - B: vertex of triangle ABC - C: vertex of triangle ABC - D: vertex of triangle SDA - S: vertex of triangle SDA

Now, let's analyze the given information: - VS = AD (Given) - VS is parallel to AD (Given)

To prove that triangle ABC is congruent to triangle SDA, we need to show that: - AB = SD - BC = DA - ∠ABC = ∠SDA

Let's start with the first condition: - AB = SD

To prove this, we can use the fact that VS is parallel to AD. This implies that angle VSB is equal to angle SDA (corresponding angles). Additionally, we know that VS = AD. Therefore, triangle VSB is congruent to triangle SDA by the Side-Angle-Side (SAS) congruence criterion. This means that AB = SD.

Next, let's move on to the second condition: - BC = DA

To prove this, we can use the fact that VS is parallel to AD. This implies that angle VSC is equal to angle SAD (corresponding angles). Additionally, we know that VS = AD. Therefore, triangle VSC is congruent to triangle SAD by the Side-Angle-Side (SAS) congruence criterion. This means that BC = DA.

Finally, let's prove the third condition: - ∠ABC = ∠SDA

To prove this, we can use the fact that VS is parallel to AD. This implies that angle VSC is equal to angle SAD (corresponding angles). Additionally, we know that VS = AD. Therefore, triangle VSC is congruent to triangle SAD by the Side-Angle-Side (SAS) congruence criterion. This means that angle ABC is equal to angle SDA.

Since all three conditions are satisfied, we can conclude that triangle ABC is congruent to triangle SDA.

Here is a diagram to illustrate the congruence of the triangles:

      A _______ B
       |       |
       |       |
       |_______|
      S         D

In the diagram, AB is congruent to SD, BC is congruent to DA, and angle ABC is congruent to angle SDA.

I hope this explanation helps! Let me know if you have any further questions.