Determine if the following triangles are similar or not.
a) A rectangular triangle and an equilateral triangle.
b) Two triangles with same angles but different sides.
c) Two triangles whose sides are proportional.
See development and solution
Development:
a) An equilateral triangle and a rectangular triangle can only have an equal angle at the most, therefore because of the fourth property of similarity, they are not similar.
b) In virtue of the fourth property of similarity, they are similar because they have at least two equal angles.
c) In virtue of the fifth property of similarity, the triangles are similar.
Solution:
Therefore, we have:
a) Not similar
b) Similar
c) Similar