Question

Let the line segments ab and cd intersect at o in such a way that equals to audi and ab = ac prove that is equals to bd but ac may not be parallel to bd

Answer 1

Given, OA = OD and OB = OC

To prove: AC = BD and AC mayn't be parallel to BD.

Proof:

In Δ AOC and Δ BOD, we have

OA = OD [given]

∠COA = ∠DOB [vertically opposite angles]

OB = OC  [given]

⇒ Δ AOC Δ BOD  [SAS congruency]

⇒ AC = BD [c.p.c.t]

Again, ∠OAC = ∠ODB  [c.p.c.t]
and ∠OCA = ∠OBD  [c.p.c.t]
Therefore, ∠OAC may not be equal to ∠OBD.
Hence, AC may not be parallel to BD.

[Hence proved]

Answer 2

Answer:

Step-by-step explanation:

Given, OA = OD and OB = OC

To prove: AC = BD and AC mayn't be parallel to BD.

Proof:

In Δ AOC and Δ BOD, we have

OA = OD [given]

∠COA = ∠DOB [vertically opposite angles]

OB = OC  [given]

⇒ Δ AOC Δ BOD  [SAS congruency]

⇒ AC = BD [c.p.c.t]

Again, ∠OAC = ∠ODB  [c.p.c.t]

and ∠OCA = ∠OBD  [c.p.c.t]

Therefore, ∠OAC may not be equal to ∠OBD.

Hence, AC may not be parallel to BD.