UPTET Paper 1 2013 Solved Paper

Concept:In a rhombus, the diagonals bisect each other at right angles. This creates four right triangles using half of each diagonal.Explanation:Consider rhombus ABCD with diagonals AC and BD intersecting at O at 90°. Since diagonals bisect each other, $AO = \frac{AC}{2}$ and $BO = \frac{BD}{2}$. In right triangle AOB, by Pythagoras theorem: $AB^2 = AO^2 + BO^2$ Substitute the half‑diagonals: $AB^2 = \left(\frac{AC}{2}\right)^2 + \left(\frac{BD}{2}\right)^2 = \frac{AC^2}{4} + \frac{BD^2}{4}$ Multiply both sides by 4: $4AB^2 = AC^2 + BD^2$ Answer:Option C: $AC^2 + BD^2 = 4AB^2$