Question

Use the image to answer the question.

A triangle is labeled clockwise from the left vertex as upper A upper B upper C. Midpoints are drawn and connected by lines within the triangle.

Consider △ABC
where D
is the midpoint of AB¯¯¯¯¯¯¯¯
and F
is the midpoint of AC¯¯¯¯¯¯¯¯
. In order to start the proof of the Triangle Midsegment Theorem, which triangles should Jamal prove are similar?

Option #1: △ADF
and △DBC

Option #2: △FDC
and △DBC

Option #3: △FDC
and △ABC

Option #4: △ADF
and △ABC

(1 point)

Answer 1

Option #4.

Reason: D and F are midpoints so AD/AB = AF/AC = 1/2. Triangles ADF and ABC share angle A, and the two adjacent sides are proportional, so △ADF ~ △ABC. From that similarity, corresponding angles give ∠ADF = ∠ABC, so DF ∥ BC (the midsegment result).