<5 ≅ <7

A Transitive property
B same side interior angles
C corresponding angles
D Definition of Parallel lines

C corresponding angles

The correct answer is C: corresponding angles.

To understand why <5 is congruent (≅) to <7, we need to know about the concept of corresponding angles. Corresponding angles are a pair of angles that are in similar positions at the intersection of two lines and a transversal (a line that cuts across two or more lines).

In this case, <5 and <7 are both angles on the same side of the transversal and are in a corresponding position with respect to their intersecting lines. The transversal creates a pair of parallel lines, and when two lines are parallel, the corresponding angles formed are congruent.

To prove that <5 is congruent to <7 using the concept of corresponding angles, we can consider the following steps:

1. Draw two parallel lines, labeled line a and line b.
2. Draw a transversal line that intersects both line a and line b, labeled line c.
3. Identify the angles formed by the transversal and the parallel lines. In this case, <5 and <7 are the corresponding angles.
4. Use the corresponding angles property, which states that when two parallel lines are intersected by a transversal, the corresponding angles formed are congruent.
5. Therefore, <5 and <7 are congruent, which can be represented as <5 ≅ <7.

By using the concept of corresponding angles, we can confidently conclude that <5 is congruent to <7 in this scenario.