Question

ОТРЕЗКИ АС И ВД ПЕРЕСЕКАЮТСЯ В ТОЧКЕ М ,АВ ПАРАЛЛЕЛЬНА СД ,МД=МВ.Докажите ,что АМ=МС СРОЧНО!!!!!

Answer 1

Углы СМД и ВМА будут равны как вертикальные. Угол ДСМ равен углу ВАС как накрестлежащие, угол СДМ равен углу АБД как накрест лежащие, значит треугольники подобны /все углы равны/. Но т.к. есть условие, что МД=МВ, то и АМ=МС как стороны в равных треугольниках. (АМ и МС заключены между равными углами (угол М общий и угол С=А), значит именно АМ будет равно МС)
Несколько кривое объяснение, извините

Answer 2

Problem Analysis

The problem states that line segments AB and CD intersect at point M, and line segment AV is parallel to SD. It is also given that MD = MV. The task is to prove that AM = MC.

Proof

To prove that AM = MC, we can use the concept of similar triangles. Let's analyze the given information and use it to establish the required equality.

1. Line segment AV is parallel to SD. 2. MD = MV.

From the given information, we can conclude that triangle AMD is similar to triangle MCV. This is because they share an angle at M and have parallel sides (AV and SD) and a pair of equal sides (MD = MV).

Using the concept of similar triangles, we know that the ratio of corresponding sides of similar triangles is equal. Therefore, we can set up the following proportion:

AM / MC = MD / MV

Since MD = MV, we can substitute this value into the equation:

AM / MC = MD / MD

Simplifying the equation, we get:

AM / MC = 1

This implies that AM = MC, which is what we needed to prove.

Therefore, we have successfully proven that AM = MC.

Conclusion

In conclusion, we have shown that line segments AM and MC are equal in length. This was proven using the concept of similar triangles, as the given information allowed us to establish the similarity between triangles AMD and MCV.