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.
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.
Steps-
-Draw line segment PQ of length 18 cm. From P draw ray PL which makes angle 60∘ with PQ using protractor. Similarly draw ray QM which makes angle 60∘ with PQ.
-Using angle bisector construction method, draw angle bisectors for angles APQ and angle AQP. Let these 2 angle bisectors meet at A.
-Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.
-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∘. 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-
-Draw line segment PQ of length 18 cm. From P draw ray PL which makes angle 60∘ with PQ using protractor. Similarly draw ray QM which makes angle 60∘ with PQ.
-Using angle bisector construction method, draw angle bisectors for angles APQ and angle AQP. Let these 2 angle bisectors meet at A.
-Using perpendicular bisector construction method draw perpendicular bisectors DE for AP and FG for AQ respectively.
-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∘. 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.
