Answer:
The three of them are similar.
Step-by-step explanation:
1- Triangle A and Triangle B have two same angles, 37° and 47°, which means the two angles are congruent. According to the Angle Angle Theorem (AA), in two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.
2- First, place both triangles correctly. When you do it, you'll notice that 24≅12, 32≅16, and 9≅4.5:
- 24/12 = 2 ✓
- 32/16 = 2 ✓
- 9/4.5 = 2 ✓
According to Side-Side-Side Theorem (SSS), if the measures of corresponding sides are known, then their proportionality can be calculated. If all three pairs are in proportion, then the triangles are similar.
3- Here, the triangle shows in each one two different angles, sharing only one which is 55°. To know if they are congruent, you can add the two different angles that show both triangles, 72° and 53°, with the 55°. If it gives 180, it means the can be congruent:
. This is proved by the fact that the distance between each corner ABC to the mirror line equals to the distance between the mirror line to A'B'C'.
