Converse of BPT and using it sheet3-mark answer frameIn ΔABC, D and E lie on AB and AC. AD = 1.8 cm, DB = 5.4 cm, AE = 2 cm and EC = 6 cm. Show that DE ∥ BC.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found. Given: AD = 1.8 cm, DB = 5.4 cm, AE = 2 cm, EC = 6 cm. To show: DE ∥ BC.
- 2 · Draw the figure. Draw ΔABC with D on AB and E on AC. Join DE and write the four lengths on the sides.
- 3 · Write the formula or theorem. Converse of BPT: if a line divides two sides of a triangle in the same ratio, it is parallel to the third side.
- 4 · Find both ratios.
- AD/DB = 1.8/5.4 = 1/3
- AE/EC = 2/6 = 1/3
- 5 · Compare them. AD/DB = AE/EC = 1/3
- 6 · Check and box the answer. Therefore DE ∥ BC (by the converse of BPT).
Scoring tip: Name the theorem in brackets. Writing 'by BPT' instead of 'by the converse of BPT' can cost a mark.
