Similar triangles: criteria and properties sheet5-mark answer frameA street lamp is 4.8 m above the ground. A girl 1.6 m tall stands 6 m from the foot of the lamp post. Find the length of her shadow.
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 Lamp height LB = 4.8 m, girl's height GF = 1.6 m, BF = 6 m. Find her shadow FS = x.
- 2 · Draw the figure Ground line B, F, S. Lamp post LB at B and girl GF at F, both vertical. Join L to S through G.
- 3 · Write the formula or theorem ΔSFG ~ ΔSBL by AA: ∠S is common and ∠SFG = ∠SBL = 90°. So GF/LB = SF/SB.
- 4 · Substitute 1.6/4.8 = x/(x + 6), so 1/3 = x/(x + 6).
- 5 · Solve
- 6 · Check and box the answer Check: 3/(3 + 6) = 3/9 = 1/3. Her shadow is 3 m long.
Scoring tip: Name the two similar triangles in matching order and give the AA reason. Most marks go for the correct ratio, not only the answer.
