The relationship in the diagram that is true is ΔRMS ≅ ΔRQS by the AAS postulate. The correct option is B.
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 the length of line segment AB, and so on for others).
For the given figure, if the two triangles are needed to be proven congruent then we can write,
In ΔRMS and ΔRQS,
RS ≅ RS {Common side for both the triangle}
∠MRS ≅ ∠QRS {RS bisect the ∠MRQ}
∠RMS ≅ ∠RQS {Given the two angles are equal}
Therefore, using the AAS postulate the two triangles can be said to be congruent.
Thus, ΔRMS ≅ ΔRQS
Hence, the relationship in the diagram that is true is ΔRMS ≅ ΔRQS by the AAS postulate.
Learn more about Congruent Triangles here:
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