In the rhombus ABCD, points E and F are the midpoints of the sides BC and CD, respectively. Prove that AE = AF.
| April 18, 2021 | education
Let us prove that triangles ABE and ADF are equal.
Since all sides of a rhombus are equal, AB = AD. Since the points E and F are the midpoints of the segments CB and CD, the segment BE = FD.
In a rhombus, the opposite angles are equal, then the angle ABC = ADC, therefore, the triangles ABE and ADF are equal on both sides and the angles between them. Since the triangles ABE and ADF are equal, then AE = AF, as required.
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