CTET Paper II (Mathematics and Science) May 2016 Solved Paper

Concept:For a quadrilateral to be constructed, the given measurements must satisfy triangle inequality and angle sum conditions. If three points are collinear, no quadrilateral is formed.Explanation:Check each case for feasibility:Case A: Two adjacent sides (AB, BC) and three angles are given. The sum of angles at A, B, C is $60^\circ + 105^\circ + 105^\circ = 270^\circ$. Since the sum of all interior angles of a quadrilateral is $360^\circ$, the fourth angle $\angle D = 90^\circ$. This case is possible.Case B: Three sides (AB, BC, AD) and two angles (A, B) are given. Using the given data, we can construct triangle ABD and then locate C. This is possible.Case C: All four sides and one diagonal AC are given. Check triangle ABC: $AB + BC = 5 + 3.5 = 8.5$ cm, which equals AC. Points A, B, and C lie in a straight line. Thus, no triangle forms, and quadrilateral ABCD cannot be constructed.Case D: Four sides (AB, BC, CD, AD) and diagonal BD are given. Check triangles ABD and BCD: Both satisfy triangle inequality (e.g., $AB + AD > BD$, etc.). Construction is possible.Answer:Quadrilateral construction is not possible in case C (Option C).