Proving Two Lines Are Parallel
Part of Vectors (Geometry Proofs) — GCSE Mathematics
This deep dive covers Proving Two Lines Are Parallel within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 11
Practice
14 questions
Recall
12 flashcards
Proving Two Lines Are Parallel
Two vectors are parallel if one is a scalar multiple of the other. That is, vector p is parallel to vector q if p = kq for some non-zero scalar k.
Method for a proof question:
- Express both direction vectors in terms of a and b by following paths through the diagram.
- Simplify both vectors.
- Show that one is a scalar multiple of the other and state what the scalar is.
- Write a concluding sentence: "Since PQ = k×RS, PQ is parallel to RS."
Worked Example: In triangle OAB, OA = a, OB = b. P is the midpoint of OA. Q is the midpoint of OB. Prove PQ is parallel to AB.
PQ = PO + OQ = -½a + ½b = ½(-a + b) = ½AB
Since PQ = ½AB, PQ is parallel to AB (and half its length).