IM Geo.3.5 Lesson: Splitting Triangle Sides with Dilation, Part 1

Here’s a triangle with midpoints , , and .  What do you notice? What do you wonder?

Here’s a triangle . Points and are the midpoints of 2 sides. Convince yourself triangle  is a dilation of triangle . What is the center of the dilation? What is the scale factor?

Convince your partner that triangle  is a dilation of triangle , with the center and scale factor you found.

With your partner, check the definition of dilation on your reference chart and make sure both of you could convince a skeptic that  definitely fits the definition of dilation.

Convince your partner that segment  is twice as long as segment .

Prove that . Convince a skeptic.

Here’s a triangle .  is  of the way from  to .  is  of the way from  to .  What can you say about segment , compared to segment ? Provide a reason for each of your conjectures.

How does  compare to ?

Are , , and  collinear? Explain or show your reasoning.