ABCD is a rhombus,EABF is a straight line such that Ea=AB=BF.prove that Ed and FC when produced meet at right angles.
Dear student,
Consider X as O according to the figure in the question provided.
Let us observe the following figure.
Consider the triangles, .
Since the sides EA = AB (Given), (corresponding angles), and AD = BC (sides of the rhombus), by Side-Angle-Side congruency, the triangles are congruent.
Therefore, the corresponding parts of corresponding triangles are also equal.
Thus,.
Consider the triangles, .
Since the sides BF = AB (Given), (corresponding angles), and AD = BC (sides of the rhombus), by Side-Angle-Side congruency, the triangles are congruent.
Therefore, the corresponding parts of corresponding triangles are also equal.
Thus,.
In ,
We have,
Thus,