Lesson Worksheet: Parallel Lines and Transversals: Other Relationships Mathematics

In this worksheet, we will practice applying the angle relationships between a pair of parallel lines and a transversal to establish and use other relationships between parallel lines and transversals.


True or False: If three or more parallel lines cut off congruent segments on one transversal, then they cut off equal segments on every transversal.

  • AFalse
  • BTrue


Given that 𝑋𝐿=9cm, find the length of 𝑋𝑍.


Given that 𝐴𝐷=6 and 𝑍𝐿=𝐶𝐷, find 𝑋𝑍+𝑌𝐿.


True or False: In the given figure, if 𝐴𝐵=𝐵𝐶=𝐶𝐷, then 𝑋𝑌=𝑌𝑍=𝑍𝐿.

  • ATrue
  • BFalse


Fill in the blank: If 𝐴𝐵𝐶𝐷 and 𝐴𝐵𝐸𝐹, then 𝐶𝐷𝐸𝐹.

  • A
  • B=
  • C


If 𝐴𝐵𝐶𝐷 and 𝐸𝐹𝐶𝐷, which of the following is correct?

  • A𝐴𝐵 is perpendicular to 𝐶𝐷.
  • B𝐸𝐺 bisects line 𝐴𝐵.
  • C𝐸𝐹 bisects line segment 𝐶𝐷.
  • D𝐴𝐵 is parallel to 𝐸𝐺.
  • E𝐴𝐵 is perpendicular to 𝐸𝐺.


If 𝐴𝐵𝐶𝐷𝐸𝐹 and 𝐶𝐸=2cm, find 𝐴𝐸.


If 𝐹 is a point on 𝐴𝐵 and 𝐸 is a point on 𝐶𝐷, 𝐴𝐵𝐸𝐹 and 𝐶𝐷𝐸𝐹, which of the following is correct?

  • A𝐸𝐹 bisects 𝐶𝐷.
  • B𝐴𝐵 is perpendicular to 𝐶𝐷.
  • C𝐸𝐹 bisects 𝐴𝐵.
  • D𝐴𝐵 is parallel to 𝐸𝐹.
  • E𝐴𝐵 is parallel to 𝐶𝐷.


Consider triangle 𝐴𝐶𝐵 and lines 𝐴𝑀 and 𝐸𝐷, which are parallel to 𝐶𝐵.

Find the length of 𝐴𝐵.

Find the measure of 𝐴𝐵𝐶.


If 𝐵𝐹𝐴𝐵, 𝐵𝐹𝐶𝐷, and 𝐵𝐹𝐸𝐹, find the length of 𝐴𝐶, where 𝐵𝐷=𝐷𝐹=3cm and 𝐴𝐸=12cm.

This lesson includes 1 additional question and 45 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.