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-I: AB is parallel to DC
Statement-II: AD is parallel to BC
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question can be answered even without using both the Statements✓ Correct
Explanation
If AC bisects both ∠A and ∠C, then triangles ABC and ADC share AC, with ∠BAC = ∠DAC and ∠BCA = ∠DCA. By ASA, △ABC ≅ △ADC, hence AB = AD and CB = CD. So AB/DC = AD/BC reduces to AB/CD = AD/CB, which is true since AB = AD and CD = CB. This conclusion follows from the question itself, without needing either statement.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →
Want more CDS practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English