Through construction, explore if it is possible to construct an equilateral triangle that is (i) right-angled (ii) obtuse-angled. Also construct an isosceles triangle that is (i) right-angled (ii) obtuse-angled.
Equilateral triangle: right-angled?
Not possible. All angles in equilateral triangle are 60° (acute).
Equilateral triangle: obtuse-angled?
Not possible. All angles in equilateral triangle are 60° (acute).
Isosceles triangle: right-angled?
Possible. Example: angles 90°, 45°, 45°. The equal angles are 45° each.
Isosceles triangle: obtuse-angled?
Possible. Example: angles 100°, 40°, 40°. The obtuse angle is between the two equal sides.
Explanation
(i) Equilateral triangles have all angles = 60°, which is acute. (ii) Equilateral triangles have all angles = 60°, which is acute. (iii) Right-angled isosceles triangle has the right angle between the two equal sides. (iv) Obtuse-angled isosceles triangle has the obtuse angle between the two equal sides.