Question

Are the two triangles similar? If yes, state the theorem that proves it: AA, SSS, SAS and if no, state no

I got my answer as SAS but my friends say it’s AA because it’s isosceles? Help please

Answer 1

To determine whether two triangles are similar, we need to check if their corresponding angles are congruent and their corresponding sides are proportional.

If two triangles have two pairs of congruent angles, then we can use the AA (angle-angle) theorem to prove that they are similar.

On the other hand, if two triangles have all three pairs of corresponding sides proportional, then we can use the SSS (side-side-side) theorem to prove that they are similar.

Finally, if two triangles have two pairs of corresponding sides proportional and the included angle between those sides congruent, then we can use the SAS (side-angle-side) theorem to prove that they are similar.

In your case, since you have an isosceles triangle, it means that two of its sides are congruent, and thus, we can say that the triangles are similar by using the SAS theorem, which stands for Side-Angle-Side.

Therefore, your answer is correct, and your friends are also correct in saying that the triangles are similar by using the AA theorem, as an isosceles triangle has two pairs of congruent angles. However, in this case, the SAS theorem is more appropriate as we have a known side and angle.

Answer 2

it can be both angle angle as well as sise angle side . angle angle cause the two sides are equal.

. but when you got in this situation you must go with angle angle