Question

Through C construct a parallel to AB.

Through A construct a parallel to BC.
Through B construct a parallel to AC.
Extend these lines to form a new triangle.
What relationship exists between the
two triangles?
A
C
B

Answer 1

new triangle is similar to and 2 times the size of the original

Explanation:

You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.

Construction

The attachment shows the described construction.

Relationship

The sides of the original triangle are midsegments of the new triangle, so the new triangle is ...

• scaled up by a factor of 2 (has 4 times the area)
• similar to the original
• rotated 180° about the common centroid of the two triangles