ZDAC = ZBAD.
What is the length of CD?
Round to one decimal place.

3.4

Step-by-step explanation:

The angle bisector theorem states that for a triangle that is bisected, the ratio between the two edges in each of the triangles that form are proportional to each other.

For this triangle, the bisector splits the triangle into ΔABD and ΔACD. The edges of ΔABD are BD and AB, while the edges of ΔACD are CD and AC. Therefore, we can say that BD/AB = CD/AC . Note that both parts of line that is bisected (BC) are on top, while the other edge sides are on the bottom. *

BD/AB = CD/AC

2.6/4.9 = ? / 6.5

multiply both sides by 6.5 to isolate the ?

2.6 * 6.5 / 4.9 = ? ≈ 3.4

* this can also be rearranged so that AB/BD = AC/CD, but it is vital to ensure that either both sides that are part of the larger triangle are on top or both parts of the bisected line are on top