Construct a triangle ABC, in which ∠B = 60∘, ∠C = 60∘ and AB + BC+ CA = 18 cm. What type of triangle is this? Find the length of each side by calculation. Verify the calculation from the construction. [4 MARKS]
Construct a triangle ABC, in which ∠B = 60∘, ∠C = 60∘ and AB + BC+ CA = 18 cm. What type of triangle is this? Find the length of each side by calculation. Verify the calculation from the construction. [4 MARKS]
Steps : 1 Mark
Construction : 3 Marks
Steps :
1. Draw line segment PQ of length 18 cm. From P draw ray PL which makes angle 60∘ with PQ. Similarly draw ray QM which makes angle 60∘ with PQ.
2. Using angle bisector construction method, draw angle bisectors for angles LPQ and angle MQP. Let these 2 angle bisectors meet at A.
3. Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.
4. Let the point where DE meets PQ be B and let the point where FG meets PQ be C. Join AB and AC. The required triangle is triangle ABC.
2 angles of the triangle are 60∘.So the 3rd angle will also be 60∘. Hence the triangle is an equilateral triangle. All 3 sides are equal and their lengths are 6 cm each.
This can be verified by the inspecting the constructed figure.
Steps : 1 Mark
Construction : 3 Marks
Steps :
1. Draw line segment PQ of length 18 cm. From P draw ray PL which makes angle 60∘ with PQ. Similarly draw ray QM which makes angle 60∘ with PQ.
2. Using angle bisector construction method, draw angle bisectors for angles LPQ and angle MQP. Let these 2 angle bisectors meet at A.
3. Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.
4. Let the point where DE meets PQ be B and let the point where FG meets PQ be C. Join AB and AC. The required triangle is triangle ABC.
2 angles of the triangle are 60∘.So the 3rd angle will also be 60∘. Hence the triangle is an equilateral triangle. All 3 sides are equal and their lengths are 6 cm each.
This can be verified by the inspecting the constructed figure.
