Let's go through the statements one at a time.

Statement A

If $A,$ $B,$ and $C$ are coplanar, they all lie on the same plane. Let's highlight these points in the diagram.

From the diagram, we see that $A,$ $B,$ and $C$ all lie on Plane $T .$ Therefore the three points are all coplanar, which means statement $A$ is true.

Statement B

Let's highlight $B C$ in our diagram.

From the diagram, we see that $B C$ runs where the two planes intersect. Therefore, statement $B$ is true.

Statement C

Let's highlight $A B$ and $C D .$

From the diagram, we see that $A B$ and $C D$ are on different planes and not intersecting. Therefore, this is a false statement.

Statement D

If $H,$ $F,$ and $D$ are coplanar, they all lie on the same plane. Let's highlight these points in the diagram.

From the diagram, we see that $H,$ and $D,$ lie on Plane $S,$ while $F$ lies on Plane $T .$ Therefore the three points are not coplanar, which means statement $D$ is false.

Statement E

The symbol $⊥$ means perpendicular. If the planes are perpendicular, they intersect each other at a $9 0^{\circ}$ -angle.

From the diagram we see that $A B,$ which runs along Plane $T,$ is at a right angle to Plane $S .$ Therefore, Plane $T$ and Plane $S$ are perpendicular, which means the statement is true.

Statement F

Let's highlight $\overline{H C}$ in the diagram.

Point $B$ bisects $\overline{H C}$ if it cuts the segment in two congruent halves. Examining the diagram, we cannot see anything that indicates that this is the case, which means we cannot conclude this.

Statement G

Let's mark $∠ A B H$ and $∠ H B F$ in the diagram.

Since $A B$ and $H C$ intersect at point $B,$ and $∠ A B H$ and $∠ H B F$ are adjacent angles with noncommon sides that are opposite rays, we know these angles form a linear pair.

Statement H

Let's highlight $A F$ and $C D$ in the diagram.

Note that $A B$ is on Plane $T$ and $C D$ is on Plane $S .$ Additionally, since $A B$ is perpendicular to Plane $S,$ we know that $A B$ and $C D$ has to be perpendicular as well. Therefore, this is something that we can conclude.

Exercise