The two triangles are congruent and it can be proved using ASA postulate. The correct option is A.
What are congruent triangles?
Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
For the two triangles to be congruent we can write the following condition,
In ΔWTU and ΔUVW,
WU ≅ WU {The common side of the two triangles}
∠TUW ≅ ∠VUW {Given}
∠TWU ≅ ∠VWU {Given}
Since the measure of the two angles in two triangles is the same, also, the length of the side between the two angles will be equal for both the triangles.
Therefore, the two triangles are congruent and it can be proved using ASA postulate.
Learn more about Congruent triangles:
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