To determine the similarity between the two triangles, we can start by summarizing the information given for each triangle.
Triangle 1:
- Angles: \( A, B, C \)
- Given: \( m∠A = 47° \) and \( m∠B = 36° \)
To find angle \( C \):
\[ m∠C = 180° - m∠A - m∠B = 180° - 47° - 36° = 97° \]
Thus, we have:
- \( m∠A = 47° \)
- \( m∠B = 36° \)
- \( m∠C = 97° \)
Triangle 2:
- Angles: \( G, H, J \)
- Given: \( m∠G = 36° \) and \( m∠J = 97° \)
To find angle \( H \):
\[ m∠H = 180° - m∠G - m∠J = 180° - 36° - 97° = 47° \]
Thus, we have:
- \( m∠G = 36° \)
- \( m∠H = 47° \)
- \( m∠J = 97° \)
Comparing the Angles: Now we can list the angles of both triangles:
Triangle 1:
- \( m∠A = 47° \)
- \( m∠B = 36° \)
- \( m∠C = 97° \)
Triangle 2:
- \( m∠G = 36° \)
- \( m∠H = 47° \)
- \( m∠J = 97° \)
Identifying Corresponding Angles:
- \( m∠A = 47° \) corresponds to \( m∠H = 47° \)
- \( m∠B = 36° \) corresponds to \( m∠G = 36° \)
- \( m∠C = 97° \) corresponds to \( m∠J = 97° \)
Since all corresponding angles are equal, we can conclude that Triangle 1 and Triangle 2 are similar by the Angle-Angle (AA) similarity postulate.
Thus, the two triangles are similar because they have the same angles, which means their shapes are identical, even if their sizes may differ.