Answer:
1. Triangle 1: 55°, 45°
Triangle 2: 55°, 80°
2. Triangle 1: 105°, 23°
Triangle 2: 52°, 105°
3. Triangle 1: 99°, 41°
Triangle 2: 40°, 99°
Step-by-step explanation:
To determine if two triangles are similar, we can use the Angle-Angle (AA) similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
Let's find the third angle in each pair of triangles:
Triangle 1: 55°, 45°
Third angle = 180° - (55° + 45°) = 80°
Triangle 2: 55°, 80°
Third angle = 180° - (55° + 80°) = 45°
Since the angles in both triangles are the same, Triangle 1 is similar to Triangle 2.
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Triangle 1: 105°, 23°
Third angle = 180° - (105° + 23°) = 52°
Triangle 2: 52°, 105°
Third angle = 180° - (52° + 105°) = 23°
Since the angles in both triangles are the same, Triangle 1 is similar to Triangle 2.
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Triangle 1: 103°, 32°
Third angle = 180° - (103° + 32°) = 45°
Triangle 2: 103°, 25°
Third angle = 180° - (103° + 25°) = 52°
Since the angles in both triangles are not the same, Triangle 1 is not similar to Triangle 2.
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Triangle 1: 99°, 41°
Third angle = 180° - (99° + 41°) = 40°
Triangle 2: 40°, 99°
Third angle = 180° - (40° + 99°) = 41°
Since the angles in both triangles are the same, Triangle 1 is similar to Triangle 2.
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Triangle 1: 73°, 47°
Third angle = 180° - (73° + 47°) = 60°
Triangle 2: 47°, 30°
Third angle = 180° - (47° + 30°) = 103°
Since the angles in both triangles are not the same, Triangle 1 is not similar to Triangle 2.
[tex]\hrulefill[/tex]
Therefore, the correct pairs of similar triangles are:
1. Triangle 1: 55°, 45°
Triangle 2: 55°, 80°
2. Triangle 1: 105°, 23°
Triangle 2: 52°, 105°
3. Triangle 1: 99°, 41°
Triangle 2: 40°, 99°
