To prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.
What is an equilateral triangle?
A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
Here, we have
AEC is a triangle in which B∈ AC and D∈ EC
Such that,
∠ABE = 90°,
∠ADE = 90°,
Also, BC = CD
Now, we have to prove that :
Δ ABE is congruent to Δ EDA
Proof :
If EAC is an equilateral triangle,
By the property of an equilateral triangle,
EA = AC = EC
If AC = EC
AB + BC = ED + CD
AB + CD = ED + CD
AB = ED
Also, AE = AE ( common segment )
Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,
Then, the other legs must be equal,
That is, BE = DA,
Hence, by the SSS postulate of congruence,
Δ ABE ≅ Δ EDA
Hence, to prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.
To learn more about the equilateral triangle from the given link
brainly.com/question/15294703
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