Which congruence statement is correct?

2 scalene triangles MDQ and SBR are given. Side MQ and SR are equal in length. Measure angle DMQ is equal to SRB and measure angle MDQ is equal to SBR.

A. △DMQ ≅ △SRB
B. △MDQ ≅ △RBS
C. △QDM ≅ △SRB
D. △MQD ≅ △SBR

1 answer

To determine which congruence statement is correct based on the information provided, we need to analyze the triangles and the given elements.

We know:

  • Side MQ is equal to side SR (MQ = SR)
  • Measure angle DMQ is equal to measure angle SRB (∠DMQ = ∠SRB)
  • Measure angle MDQ is equal to measure angle SBR (∠MDQ = ∠SBR)

From this information, we can apply the Angle-Side-Angle (ASA) congruence criterion, which states that if two angles and the side between them are equal in two triangles, then the triangles are congruent.

Given the relationships:

  • ∠DMQ (first angle) and ∠MDQ (second angle) correspond to angles in triangle SRB.
  • The side MQ corresponds to side SR.

These relationships indicate that:

  1. Side MQ = Side SR
  2. ∠DMQ = ∠SRB
  3. ∠MDQ = ∠SBR

With this configuration, we can make the conclusion as follows:

Triangle DMQ will correspond with triangle SRB based on ASA.

Thus, the correct statement is:

A. △DMQ ≅ △SRB