Question

a line that intersects two or more lines.
example: ________
transversals
examples

Explanation:

Step1: Recall the definition of a transversal

A transversal is a line that intersects two or more lines (usually parallel lines in common geometric contexts) at distinct points.

Step2: Provide an example

For example, if we have two parallel lines \( l \) and \( m \), and a line \( n \) that crosses both \( l \) and \( m \), then line \( n \) is a transversal. A common real - life - inspired example can be thought of as a road (the transversal) crossing two parallel train tracks (the two lines being intersected). In a more geometric diagram - based example, if we have two horizontal parallel lines and a slanted line that cuts through both of them, that slanted line is a transversal. Let's take a simple case: suppose we have line \( AB \) and line \( CD \) parallel to each other, and line \( EF \) intersects \( AB \) at point \( G \) and \( CD \) at point \( H \). Then \( EF \) is a transversal of \( AB \) and \( CD \). A very basic example to write in the blank could be a line crossing two parallel lines, for instance, if we consider the standard parallel lines cut by a transversal diagram, we can say a line like \( t \) that cuts through two parallel lines \( p \) and \( q \) (where \( p\parallel q \)) is a transversal. So we can write an example such as "A line crossing two parallel horizontal lines (e.g., a slanted line intersecting two parallel lines)". But in a more concise way, we can just draw or describe a simple transversal. For the blank under "Example:" for the transversal definition, we can give a geometric example: Let's say we have two parallel lines \( l_1 \) and \( l_2 \), and a line \( l_3 \) that intersects \( l_1 \) at point \( A \) and \( l_2 \) at point \( B \). Then \( l_3 \) is a transversal. So we can write "A line intersecting two parallel lines (e.g., a slanted line cutting through two horizontal parallel lines)".

Answer:

A line intersecting two parallel lines (e.g., a slanted line cutting through two horizontal parallel lines) (or a more specific example like a line crossing two parallel train tracks - inspired geometric lines)