Question

Are all isosceles triangles similar? Are all right triangle similar? Are all isosceles right triangles similar? Explain.

Please don't answer with one answer, blank or a ridiculous response. This is serious please.

And don't send links that are viruses

Please explain each one.

Answer 1

9514 1404 393

Answer:

  a) no

  b) no

  c) yes

Step-by-step explanation:

a) Isosceles triangles can have a third angle (the one that is not part of the pair of equal angles) with any value in the range 0 < α < 180°. Triangles with different angle values will not be similar.

Not all isosceles triangles are similar.

__

b) The smallest acute angle of a right triangle can have any measure in the range 0 < α ≤ 45°. Right triangles having different smallest angles will not be similar. The attachment shows dissimilar right triangles.

Not all right triangles are similar.

__

c) If the smallest acute angle of a right triangle is 45°, then both acute angles are 45°, and the right triangle is an isosceles triangle. Each such triangle will be similar to every such triangle.

All isosceles right triangles are similar.