Triangle ABCD-isosceles, points D and F- midpoints of its lateral sides, E-point at the base

| August 13, 2021 | education

Triangle ABCD-isosceles, points D and F- midpoints of its lateral sides, E-point at the base, DE || BC, EF || AB. Determinant of the form of a DBFE quadrilateral and find its perimeter if AB = 18 cm.

Since points D and F are the midpoints of the lateral sides, the segment DF is the midline of the triangle ABC.

Then DF is parallel to AC.

Consider triangles ADE and CFE. Segment AD = CF, as halves of the same lateral sides, angle BAC = BCA as angles at the base of an isosceles triangle, angle ADE = CFD = ABC as internal angles at the intersection of parallel straight lines.

Then the triangle ADE = CFD, and therefore AE = CE. Then BE is the median and the height of the triangle ABC, which means it is perpendicular to DF.

The diagonals of the quadrilateral DBFE are perpendicular, and the opposite sides are parallel, hence the quadrilateral is a rhombus.

Answer: DBFE rhombus.



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