Final answer:
The triangles ΔCDE and ΔFGH have identical angles but without information on their side lengths, we cannot determine congruency. Thus, they are not necessarily congruent.
Step-by-step explanation:
To determine if the triangles ΔCDE and ΔFGH are congruent, we need to compare the angles given and the sum of the angles in a triangle. In ΔCDE, the angles given are m∠C = 30° and m∠E = 50°. Using the fact that the sum of the angles in any triangle is 180°, we can calculate m∠D by subtracting the sum of angles C and E from 180°:
m∠D = 180° - (m∠C + m∠E) = 180° - (30° + 50°) = 100°.
Now, let's analyze ΔFGH. The angles given are m∠G = 100° and m∠H = 50°. To find m∠F, we again subtract the sum of angles G and H from 180°:
m∠F = 180° - (m∠G + m∠H) = 180° - (100° + 50°) = 30°.
Comparing the angles of both triangles, we see that they all match (∠C = ∠F, ∠D = ∠G, and ∠E = ∠H). This indicates that the triangles are similar since all corresponding angles are equal. However, without information about the side lengths, we cannot conclude that they are congruent because congruency requires both the angles and sides to be equal. Therefore, the correct answer is:
d. No, the triangles are not necessarily congruent.