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Criteria for similarity: AAA, SSS and SAS sheet
3-mark answer frame

In ΔABC, D and E are points on AB and AC with AD = 2 cm, DB = 4 cm, AE = 3 cm and EC = 6 cm. Prove that ΔADE ~ ΔABC and find DE if BC = 9 cm.

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 found. Given: AD = 2 cm, DB = 4 cm, AE = 3 cm, EC = 6 cm, BC = 9 cm. To prove: ΔADE ~ ΔABC. To find: DE.
  2. 2 · Draw the figure. Draw ΔABC with D on AB and E on AC. Join DE and mark all the lengths.
  3. 3 · Write the formula or theorem. SAS similarity criterion.
  4. 4 · Find the ratios and the common angle.
    • AB = 2 + 4 = 6 cm and AC = 3 + 6 = 9 cm
    • AD/AB = 2/6 = 1/3 and AE/AC = 3/9 = 1/3
    • ∠DAE = ∠BAC (common angle)
  5. 5 · Conclude the similarity. So ΔADE ~ ΔABC (SAS).
  6. 6 · Find DE. DE/BC = AD/AB = 1/3, so DE = 9/3 = 3 cm.
  7. 7 · Check and box the answer. ΔADE ~ ΔABC; DE = 3 cm.

Scoring tip: Name the common angle and the criterion. 'Common angle' and '(SAS)' each carry a mark.