<2 ≅ <7
A Transitive property
B same side interior angles
C corresponding angles
D Definition of Parallel lines
D Definition of Parallel lines
To determine the relationship between <2 and <7, we need to consider the given answer choices:
A) Transitive property: The transitive property states that if two angles are congruent to a third angle, then they are congruent to each other. However, the given statement "<2 ≅ <7" does not provide any information about the congruence of these angles with a third angle. Therefore, the transitive property does not apply here.
B) Same-side interior angles: Same-side interior angles are a pair of angles formed when two lines are crossed by a third line, and the angles are on the same side of the transversal. The given statement does not provide any information about the angles being same-side interior angles. Therefore, same-side interior angles do not apply here.
C) Corresponding angles: Corresponding angles are pairs of angles that lie on the same side of the transversal, in corresponding positions. Although the given statement does not explicitly mention a transversal or parallel lines, if it can be inferred that <2 and <7 are corresponding angles, then we can conclude that they are congruent. However, without further information, we cannot determine if they are corresponding angles.
D) Definition of Parallel lines: The definition of parallel lines states that if two lines are parallel, then the corresponding angles formed when a transversal intersects those lines are congruent. Again, the given statement does not explicitly mention parallel lines or a transversal, so we cannot determine if this definition applies.
In conclusion, based on the provided options, we cannot determine the specific relationship between <2 and <7.
The correct answer is C: corresponding angles.
To understand why, let's break down the question and the answer choices:
<2 ≅ <7 indicates that angle 2 is congruent to angle 7. In mathematical notation, the symbol "≅" represents congruence, meaning that the two angles are identical in measure.
Now, let's examine the answer choices:
A. Transitive property: The transitive property states that if two things are equal to the same thing, then they are equal to each other. However, in this case, we don't have two equal things. Instead, we have two equal angles.
B. Same side interior angles: Same side interior angles are angles that are on the same side of the transversal and on the inside of the two parallel lines. Here, we have only mentioned angles 2 and 7 without any mention of parallel lines or a transversal. So, this answer choice is not applicable in this context.
C. Corresponding angles: Corresponding angles are formed when a transversal intersects two parallel lines. In this case, if we assume that angles 2 and 7 are corresponding angles, it means that they are formed by the intersection of a transversal and two parallel lines. Therefore, this answer choice aligns with the given information.
D. Definition of parallel lines: The definition of parallel lines states that two lines are parallel if they are coplanar and never intersect. While this definition is related to the concept of parallel lines, it does not directly explain why angle 2 is congruent to angle 7.
Hence, the correct answer is C: corresponding angles.