Question

two triangles are similar if their corresponding angles are proportional.
true / false
explain

Answer 1

false

Answer 2

their angles should be same but sides should be proportional.

Answer 3

By definition of similar triangles, corresponding angles are congruent and corresponding sides are in proportion. That said, the answer to the quesion is false.

Answer 4

by AAA criterion they can be similar??

Answer 5

I agree with shubham.

Answer 6

For some reason, I am inclined to agree... after all, if the angle measures are proportional, they have to be congruent, given that the angle sum of a triangle is always 180 degrees.

Answer 7

Triangles are similar by the AA Postulate. It is not necessary to call it the AAA postulate because if two angles of one triangle are congruent to two angles of another triangle, the third angles are also congruent. So, AAA would be redundant.

Answer 8

Let me put it this way, suppose the angle measures of the first triangle are given by
\[\huge \alpha \ \beta \ \gamma\]then by the angle sum of triangles,
\[\huge \alpha + \beta+\gamma=180^o\]
Now the angles of the second triangle are in proportion to the first, meaning they are the angles of the first, multiplied by some constant...
\[\huge k\alpha \ k\beta \ k\gamma\]But then again, this is a triangle, so...
\[\huge k\alpha +k\beta+k\gamma=k(\alpha+\beta+\gamma)=180^o\]
Means k=1
Means the angles were congruent after all...

Answer 9

The definition of similar triangles states what similar triangles are. It is not left to interpretation.

Answer 10

Fair enough.