Question

for parts a and b, let abcd be a square with diagonals ac and bd intersecting in point f, as shown in the figure. a what is the relationship between point f and the diagonals bd and ac? a f is the midpoint of bd and ac b bd is the midpoint of f and ac c af is the perpendicular bisector of bf d f = bd + ac b what are the measures of angles bfa and afd? a ∠bfa = 90°, ∠afd = 90° b ∠bfa = 45°, ∠afd = 45° c ∠bfa = 90°, ∠afd = 0° d not enough information

Explanation:

Step1: Recall square properties

In a square, the diagonals bisect each other. So point F is the mid - point of both diagonals $\overline{BD}$ and $\overline{AC}$.

Step2: Recall diagonal - angle property

The diagonals of a square are perpendicular to each other. So $\angle BFA = 90^{\circ}$ and $\angle AFD=90^{\circ}$.

Answer:

a. A. F is the midpoint of $\overline{BD}$ and $\overline{AC}$
b. A. $\angle BFA = 90^{\circ}$, $\angle AFD = 90^{\circ}$