Construct ΔABC with BC = 6 cm, ∠A = 60° and median AM = 5 cm. Measure the altitude from A to 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 constructed Base BC = 6 cm, vertical angle ∠A = 60°, median AM = 5 cm. Construct ΔABC and measure the altitude from A.
2 · Draw the rough figure Sketch ΔABC, the circle through B and C, and the median AM. Write all the given values.
3 · Write the theorem it uses Alternate segment theorem: the arc above BC holds the 60° angle.
4 · Draw the base and the circle
BC = 6 cm; ray BX below BC with ∠CBX = 60°
BY ⊥ BX; the perpendicular bisector of BC meets BY at O and BC at M
Circle with centre O and radius OB
5 · Locate A An arc of radius 5 cm with centre M cuts the upper arc at A. Join AB and AC.
6 · Write the steps of construction Number each step in short sentences, in the order you drew them.
7 · Check and box the answer Measure ∠A = 60°. Draw AD ⊥ BC: AD ≈ 4.6 cm. Box: ΔABC is the required triangle.
Scoring tip: Draw BX below BC, so the useful arc is above BC. Keep all construction arcs, because they show your method.
