Complete the following statement. Two lines are congruent if…….
Hint: Two geometric figures are said to be congruent if one can be transformed into the other by an isometry. So take two lines$AB$and$PQ$, and keep the length the same. You will get the statement.
Congruent segments are simply lined segments that are equal in length. Congruent means equal. We indicate a line segment by drawing a line over its two endpoints. Another way to show that segments are congruent is to have a squiggly line over an equal sign. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry. Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane. In the figure above, there are two congruent line segments. Note they are laying at different angles. If you drag any of the four endpoints, the other segment will change the length to remain congruent with the one you are changing. So let us take a segment$AB$and$PQ$. For line segments, 'congruent' is similar to saying 'equals'. You could say "the length of the line $AB$equals the length of the line $PQ$". But in geometry, the correct way to say it is "line segments $AB$ and $PQ$ are congruent" or, "$AB$ is congruent to$PQ$". Rays and lines cannot be congruent because they do not have both endpoints defined, and so we have no definite length. So we get the final solution as two lines are congruent if they have the same length.
Note: Another way to show that segments are congruent is to have a squiggly line over an equal sign. The symbol for congruence is $\cong $. Also, recall that the symbol for a line segment is a bar over two letters, so the statement$AB\cong PQ$is read as "The line segment $AB$ is congruent to the line segment $PQ$".
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