2026 · Q73
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: ABCD is a quadrilateral such that AC bisects ∠A and ∠C. Is AB/DC equal to AD/BC?
Statement IAB is parallel to DC.
Statement IIAD is parallel to BC.
Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsQuadrilaterals and Polygons
- AThe Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question can be answered even without using both the Statements
Explanation
Since AC bisects both ∠A and ∠C, ΔABC≅ΔADC by ASA (common side AC with two pairs of equal adjacent angles). Hence AB=AD and BC=DC, so AB/DC=AB/BC=AD/BC identically — the equality holds with no statements at all, option D. This is why the question is answerable with no statements at all: the ASA congruence is forced by the given bisection alone.