Question

Does a line that intersects two sides of a triangle and is parallel to the third side of the triangle form two similar triangles? Use mathematical language from this course to explain your answer. Sketch a picture and label the vertices. Use the sketch in your discussion answer.

Answer 1

First let's draw a sketch of the question, using the points A, B and C to make the triangle and points D and E to create the line parallel to the third side:

Since the segments DE and BC are parallel, so the corresponding angles ADE and ABC are congruent.

Also, angle A is common to both triangles ADE and ABC.

Since we have two pairs of congruent angles, we can prove that the triangles ADE and ABC are similar by case AA (angle-angle).

Therefore the answer is YES.