Question

Question:Use the image to answer the question.A triangle is marked clockwise from the lower left vertex as $\triangle ABC$. Point $D$ is marked at the midpoint of side $\overline{AB}$. Point $F$ is marked at the midpoint of side $\overline{AC}$. A line connects midpoints $D$ and $F$. Segment $\overline{AD}$ and segment $\overline{DB}$ are marked with single congruent tick marks. Segment $\overline{AF}$ and segment $\overline{FC}$ are marked with double congruent tick marks.Which statement could be proved with the help of the figure?(1 point)Multiple Choice Options (Responses)( ) The sum of the interior angles of a triangle equals $180^\circ$.( ) A line connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.( ) The base angles of an isosceles triangle are congruent.( ) Two triangles are similar if they have two pairs of congruent angles.

Answer 1

The correct choice is: A line connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Reason: D and F are midpoints so AD = DB and AF = FC. Triangles ADF and ABC are similar (AD/AB = AF/AC = 1/2 and they share ∠A), so DF = 1/2·BC and DF ∥ BC (midpoint theorem).