The bisector of an acute angle A of parallelogram ABCD intersects side BC at point M, which divides BC
| January 27, 2021 | education
The bisector of an acute angle A of parallelogram ABCD intersects side BC at point M, which divides BC into two segments 8 cm and 12 cm. Line AM intersects the continuation of side CD at point F. Find the length of segment DF.
Determine the length of the segment BC. BC = BM + CM = 12 + 8 = 20 cm.
The bisector AM cuts off the isosceles triangle ABM from the lateral side AB, then AB = BM = 12 cm.
The lengths of the opposite sides of the parallelogram are equal, then СD = AB = 12 cm, AD = BC = 20 cm.
Triangles ABM and MFC are similar in two angles, then AB / BM = FC / CM.
12/12 = FC / 8.
FC = 8 cm.
Then DF = 12 + 8 = 20 cm.
Answer: The length of the segment DF is 20 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.
