a Similar triangles have at least two pairs of congruent angles. Congruent triangles also have the same size.
B
b Which sides are corresponding in the two triangles?
C
c How many pairs of congruent angles do you need to claim similarity?
A
a Similar, but not necessarily congruent.
B
b Similar and congruent.
Flowchart: See solution.
C
c We cannot tell if they are similar or congruent.
Practice makes perfect
a If the triangles are similar, they have the same shape. We know this is true if the triangles have at least two congruent angles. Examining the diagram, we see that this is in fact the case for our triangles.
Therefore, we know that the triangles are similar by the AA Similarity condition. If the triangles are congruent, they also have the same size. However, we do not know anything about the length of any sides in the triangles and therefore, we cannot say if they are congruent.
b Like in part A, we see that the triangles have two pairs of congruent corresponding angles. Therefore, we can claim by the AA Similarity condition that they are similar. Next, we will determine if the triangles are congruent. Let's identify corresponding sides in these triangles.
As we can see, one pair of corresponding sides are congruent. This means we can claim congruence by the AAS Congruence condition.
Flowchart
Let's show this as a flowchart.
c If two triangles are congruent, they are also similar. Therefore, we should first investigate if the triangles are similar. To claim similarity, we need to know that at least two pairs of angles in the triangles are congruent. However, in these triangles, we have only been given one pair of congruent angles.
We have no idea what measure the other angles have and, therefore, we cannot claim that they are similar.
