a We want to ensure that sailboat races are fair. To do so, we need that both boats have the same size and shape. If the sails are of the same size and shape, then the corresponding triangles are congruent.
This means that there is a congruence for the smaller sails and another for the larger sails. Let's write the congruent statement relating each triangle by using the symbol ≅, which represents congruence between two figures.
△ A B C&≅△ M N O
△DEF
&≅
△PQR
Extra
Writing a Congruence Statement
When it comes to writing a triangle congruence statement, the order in which the vertices are written is critical. Naming them in an incorrect order leads to erroneous conclusions. Consider, for example, the following congruent triangles.
Although the triangles are congruent, the congruence statement △ ABC ≅ △ MQT is incorrect. Why? Because it would lead to the following conclusions about the sides and angles.
Consequently, always be sure to list the corresponding vertices in the correct order. </statementbox>
b Segments connecting corresponding vertices themselves correspond to each other. This means that they are congruent.
A B&≅M N
B C&≅N O
A C&≅M O
D E
&≅
P Q
E F
&≅
Q R
D F
&≅
P R
c Since we know that the sails are congruent, their angles at corresponding vertices also correspond to each other. Therefore, the corresponding angles have the same measure.
∠ A&≅∠ M
∠ B&≅∠ N
∠ C&≅∠ O
∠ D&≅∠ P
∠ E&≅∠ Q
∠ F&≅∠ R
