Question

Two line segments ab and CD intersect each other at O such that AO= OB and CO= OD . Prove that AC = BD .

Answer 1

triangle aoc is congurent to triangle odb

$ao = bo (given) \\ angle \: aoc = angle \: dob \: (verticaly \: opposite \: angle) \\ co = od(given) \\ proved \: triangle \: aoc \: is \: congurent \: to \: triangle \: dob \\ ac = db(cpct)$

Answer 2

Step-by-step explanation:

Given:two line segment ab and CD intersects each other at o

AO=OB and CO=OD

To prove:AC=BD

proof: In ∆AOC and ∆DOB

AO=BO (given)

<AOC= <DOB (vertically opposite angles)

CO=OD (given)

therefore: ∆AOC ≈∆DOB (by SAS congruence rule)

therefore:AC=DB(by CPCT)