Answer:
3. False, in order for these points to be collinear, they need to lie on the same line, and since these points are spread out (only two lie on the same line), they form a plane (formed by at least three non-collinear points) which should not happen if you want points to be collinear.
4. True, angle DCJ and angle DCH are supplementary. This is because in order for there to be supplementary angles, their sums have to be equal to 180 degrees and form a straight line when put together.
5. False, segment DC is not perpendicular to line l. This is because these two do not intersect at all and in order for a line, segment, or ray to be perpendicular to another, they have to intersect each other at right angles.
6. True, segment FB is perpendicular to line n. This is because they intersect each other at right angles which defines what perpendicular is.
7. False, angle FBJ and angle JBA are not complementary. This is because these angles form to make a straight line which measures 180 degrees, meaning that they are supplementary instead of complementary. In order for there to be complementary angles, both angles have to have a sum of 90 degrees (which is represented by the right angle mark).
8. False, there is no way of telling that line m bisects angle JCH. This is because in order to identify if a ray, line etc. is a bisector of another, there has to be congruent marking symbols on both sides of the ray, line, etc. where that specific ray, line etc. intersects.
9. True, angle ABJ and angle DCH are supplementary because they have right angle markings on them indicating that each of them measures 90 degrees. In order for there to be supplementary angles, their angle measures have to sum up to 180 degrees, so when you add these two angle measures together (90 + 90) they equal 180 degrees which defines supplementary.
Biconditional statement:
A statement that is formed when you combine a true conditional and it's true converse together by an "if and only if" phrase between them.
Notation to define this:
p(hypothesis) ⇔ q(conclusion)
In this case, they give us the biconditional:
"Two angles are congruent if and only if they have the same measure."
Let's identify the p(the hypothesis) and q(the conclusion) - these are the components that make up a conditional.
We first have to break this biconditional down.
Two angles are congruent if and only if they have the same measure.
This will be the "if"/hypothesis part of our conditional statement.
Two angles are congruent if and only if they have the same measure.
This will be the "then"/conclusion part of our conditional statement.
Let's now use the format "if ____, then ____" (represented by the notation of p ⇒ q).
So:
If two angles are congruent, then they have the same measure.
This will be our conditional statement, to make it a converse we just switch the p and q around (represented by the notation of q ⇒ p).
So:
If two angles have the same measure, then they are congruent.
This will be our converse of the conditional statement.