Question

Which similarity postulate or theorem can be used to determine if the two are similar

Answer 1

Side-Angle-Side similarity Theorem

Explanation:

• If you want to know whether two triangles are similar or not, and you know the lenght of two sides and the corresponding angle between the sides, you can apply the Side-Angle-Side similarity Theorem. This theorem states that, if the mentioned angle is similar (wich is in this case, both angles equal 46º), and the lenghts of the sides that contains the angle are proportional (also the case : if we evaluate the proportion of the sides of the first triangle
  `(70)/(100)=0.7`, it is equal to the proportion of the sides of the second triangle
  `(28)/(40)=0.7`), the triangles are similar.
• The Side-Side-Side similarity Theorem states that. two triangles are similar if each side of the triangle is proportional to the corresponding side of the other triangle. To apply this theorem, you must have information about the lenghts of all the sides of the triangles, which is not the case.
• The Angle-Angle similarity Theorem states that two triangles are similar if the angles of the first triangle are congruent to two angles of the other triangle. To apply this theorem, you must count on information about the two angles of the two triangles, which is not the case.