a||b
A Transitive property
B same side interior angles
C corresponding angles
D Definition of Parallel lines
C corresponding angles
The given expression, "a||b," represents the statement that line segment a is parallel to line segment b.
If we want to establish the transitive property in this context, we need to have additional information or premises. The transitive property states that if a is parallel to b and b is parallel to c, then a is parallel to c.
The "same side interior angles" are a concept related to parallel lines. When two parallel lines are crossed by a third line (known as a transversal), the angles formed on the same side of the transversal and between the two parallel lines are called same side interior angles. However, this concept is not directly related to the given expression.
Similarly, "corresponding angles" are formed when a transversal intersects two parallel lines. Corresponding angles are located in the same position relative to the transversal and parallel lines. However, this concept is not related to the given expression either.
The definition of parallel lines states that if two lines are parallel, they never intersect. This definition directly relates to the given expression, "a||b," which states that line segment a is parallel to line segment b. Therefore, the correct answer would be D, Definition of Parallel lines.
To determine the correct statement for the given expression "a||b", we need to understand the symbols and their meanings.
The expression "a||b" is written in mathematical notation and consists of the variables "a" and "b" separated by two vertical lines. In this context, the vertical lines represent the notation for parallel lines.
Now, let's go through the options and determine which one is applicable to the given expression:
A) Transitive property: The transitive property states that if a = b and b = c, then a = c. However, the expression "a||b" does not involve any equality or logical relationship between "a" and "b". So, the transitive property does not apply here.
B) Same-side interior angles: Same-side interior angles are a property of parallel lines. When a transversal line intersects two parallel lines, same-side interior angles are formed. However, the given expression "a||b" does not explicitly mention any angles or transversal lines, so this property is not directly applicable.
C) Corresponding angles: Corresponding angles are another property of parallel lines. They are formed when a transversal line intersects two parallel lines. However, similar to option B, the given expression does not explicitly mention angles or transversal lines, so this property is not directly applicable either.
D) Definition of parallel lines: The definition of parallel lines states that two lines are parallel if they never intersect or if they lie in the same plane but never meet. This is denoted by the symbol "||". Therefore, the given expression "a||b" directly represents the definition of parallel lines.
So, the correct statement for the expression "a||b" is option D) Definition of Parallel lines.