Question

State and prove AAA (angle angle angle) criteria.

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Answer 1

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AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

From the figure given above, if ∠ A = ∠X and ∠C = ∠Z then ΔABC ~ΔXYZ.

From the result obtained, we can easily say that,

AB/XY = BC/YZ = AC/XZ

and ∠B = ∠Y

Answer 2

Answer:

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

From the figure given (I have included), if ∠ A = ∠X and ∠C = ∠Z then ΔABC ~ΔXYZ.

From the result obtained, we can easily say that,

AB/XY = BC/YZ = AC/XZ

and ∠B = ∠Y