Question

triangle def is formed by connecting the midpoints of the sides of triangle abc. the lengths of the sides are shown. what is the length of bd? a 4 units b 5 units c 6 units d 8 units

Explanation:

Step1: Recall mid - point theorem

In a triangle, the line segment joining the mid - points of two sides of a triangle is parallel to the third side and half of its length. Since $\triangle DEF$ is formed by connecting the mid - points of the sides of $\triangle ABC$, and $ED$ is parallel to $AB$ and $ED$ is half of $AB$, $EF$ is parallel to $BC$ and $EF$ is half of $BC$, $DF$ is parallel to $AC$ and $DF$ is half of $AC$. Also, $D$ is the mid - point of $BC$.

Step2: Identify the length of $BD$

Given that $CD = 5$ and $D$ is the mid - point of $BC$, then $BD=CD = 5$ (because a mid - point divides a line segment into two equal parts).

Answer:

B. 5 units