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.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

  • ATrue
  • BFalse

Q5:

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

  • A
  • B=
  • C

Q6:

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.

Q7:

If 𝐴𝐵𝐶𝐷𝐸𝐹 and 𝐶𝐸=2cm, find 𝐴𝐸.

Q8:

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.

Q9:

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

Find the length of 𝐴𝐵.

Find the measure of 𝐴𝐵𝐶.

Q10:

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.

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