haya.Learning made clear
Construction: a similar triangle with a given scale factor sheet
8-mark answer frame

ΔPQR has QR = 6 cm, PQ = 5 cm and PR = 4.5 cm. Construct a similar triangle with sides 3/5 of the corresponding sides of ΔPQR.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be constructed Given ΔPQR with QR = 6 cm, PQ = 5 cm, PR = 4.5 cm and scale factor 3/5. Construct ΔP′QR′ ~ ΔPQR.
  2. 2 · Draw the rough figure Sketch ΔPQR, the ray QX below QR with Q₁ to Q₅, and the small triangle P′QR′. Write all lengths.
  3. 3 · Write the theorem it uses A line parallel to one side of a triangle divides the other two sides in the same ratio (Thales theorem).
  4. 4 · Construct ΔPQR Draw QR = 6 cm. Cut arcs of 5 cm from Q and 4.5 cm from R. Mark P and join PQ and PR.
  5. 5 · Make the parallels
    • Ray QX below QR; mark Q₁ to Q₅ with equal arcs.
    • Join Q₅R. Through Q₃ draw a parallel to Q₅R, meeting QR at R′.
    • Through R′ draw a parallel to RP, meeting QP at P′.
  6. 6 · Write the steps of construction Number each step in short sentences, in the order you drew them.
  7. 7 · Check and box the answer Measure: QR′ = 3.6 cm, QP′ = 3 cm, P′R′ = 2.7 cm. Box: ΔP′QR′ is the required triangle.

Scoring tip: Draw thin construction lines and keep every arc. Marks go to the rough figure, the arcs and the written steps, not only the final triangle.