Question

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this? [4 MARKS]

Answer 1

Steps : 1 Mark
Construction : 3 Marks

Steps:
1. Draw line segment PQ of length 24 cm.
2. From P draw ray PL which makes angle 53.13^∘ with PQ using protractor.
3. Similarly draw ray QM which makes angle 36.87^∘ with PQ.
4. Using angle bisector construction method, draw angle bisectors for angles LPQ and angle MQP. Let these 2 angle bisectors meet at A.
5. Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.
6. Let the point where DE meets PQ be B and let the point where FG meets PQ be C. Join AB and AC.
7. The required triangle is triangle ABC.