Congruent triangles are the exact same triangles, but they might be placed at different positions. The correct option is B.
What are congruent triangles?
Congruent triangles are the exact same triangles, but they might be placed at different positions.
Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent.
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 \angle B = \angle E\\\\\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).
In the two of the given triangle, therefore, ΔADC and ΔEBC,
∠CAD = ∠CEB {Already given in the triangle}
∠ACD = ∠ ECB {It is the common angle between two triangles}
CD = CB {Already given in the triangle}
Since in the two triangles, two angles are equal and a side is equal as well, therefore, the two triangles are congruent using the AAS (Angle-Angle-Side) postulate.
Hence, the correct option is B.
Learn more about Congruent Triangles:
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