The lateral side of an isosceles triangle is 25. From a point taken at the base of this triangle
| September 27, 2021 | education
The lateral side of an isosceles triangle is 25. From a point taken at the base of this triangle, two straight lines are drawn, parallel to the lateral sides. Find the perimeter of the resulting parallelogram.
Consider a triangle CDM.
DM parallel to AB by condition, then the angle BAC = MDC as the corresponding angles at the intersection of parallel AB and DM of the secant AC, and since the angle ABC = BCA, the angle MCD = MDC, and therefore the triangle CDM is isosceles. DM = CM.
Similarly, triangle ADK is isosceles, AK = DK.
The perimeter of the parallelogram is DMBK = DM + BM + BK + DK = 2 * BK + 2 * BM = 2 * AB = 2 * 25 = 50 cm.
Answer: The perimeter of the parallelogram is 50 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
