b How can we tell by a diagram that segments are congruent?
C
c Where does BC start?
D
d What creates a plane?
A
a Yes.
B
b No.
C
c No.
D
d Yes.
Practice makes perfect
a We are given the following diagram and asked if we can conclude that A, B, and D are collinear by looking at it.
Looking at the diagram, we can see that A, B, and D all lie on the same line. This is the definition of collinear points. Therefore, we can make this conclusion.
b Using the same diagram, we are now asked if we can make the following conclusion.
AB ≅ BC
In order for two segments to be congruent, we must either be given their lengths or have marks on the diagram indicating that they are congruent segments. Since we are given neither of these things, we cannot conclude that the segments are congruent.
c This time we need to decide if we can conclude that ray BC contains point A.
A ray starts at the first point in its name.
B C ⇒ starts atB
It then goes towards the second point in its name, which is C in this case. Looking at the diagram, we can see that this is the opposite direction of A. Therefore, we cannot make this conclusion.
d Finally, we need to use the diagram to see if we can conclude that E, F, and B are coplanar. We can see on the diagram that all of these points do, in fact, lie on the plane. Therefore, they are coplanar and we can make this conclusion.
