To determine if the triangles △ABC and △MNC are similar, we can use the Angle-Angle (AA) similarity criterion for triangles, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
Given the information:
- ∠B = 27° (in triangle ABC)
- ∠MCN = 73° (in triangle MNC)
- Both triangles are right triangles.
Since both triangles contain a right angle (90°), we can find the third angles using the fact that the sum of angles in a triangle is 180°.
For triangle ABC:
- The third angle (∠A) can be calculated as follows: \[ ∠A = 180° - 90° - 27° = 63° \]
For triangle MNC:
- The third angle (∠N) can be calculated as follows: \[ ∠N = 180° - 90° - 73° = 17° \]
Now we have:
- Triangle ABC has angles of 90°, 27°, and 63°.
- Triangle MNC has angles of 90°, 73°, and 17°.
Comparing the angles:
- ∠B (27°) is not equal to ∠MCN (73°).
- ∠A (63°) is not equal to ∠N (17°).
However, since both triangles have one angle that is the same (both have a right angle), and we already calculated the other angles, we can see that this angle setup does not lead to similarity by AA or any other means.
Therefore, the correct statement regarding the similarity of the triangles is:
No, △ABC and △MNC are not similar because ∠B is not equal to ∠MCN.
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