3. Postulates and Diagrams
Sign In
Some things to keep in mind are that coplanar points lie on the same plane, bisected things are cut in half, and linear pairs are adjacent angles with noncommon sides that are opposite rays.
D and F
Let's go through the statements one at a time.
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.
Let's highlight BC in our diagram.
Let's highlight AB and CD.
From the diagram, we see that AB and CD are on different planes and not intersecting. Therefore, this is a false statement.
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.
The symbol ⊥ means perpendicular. If the planes are perpendicular, they intersect each other at a 90^(∘)-angle.
From the diagram we see that AB, 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.
Let's highlight HC in the diagram.
Point B bisects HC 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.
Let's mark ∠ABH and ∠HBF in the diagram.
Since AB and HC intersect at point B, and ∠ABH and ∠HBF are adjacent angles with noncommon sides that are opposite rays, we know these angles form a linear pair.
Let's highlight AF and CD in the diagram.
Note that AB is on Plane T and CD is on Plane S. Additionally, since AB is perpendicular to Plane S, we know that AB and CD has to be perpendicular as well. Therefore, this is something that we can conclude.