Question

of two straight line intersect each other prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle

pls help me guys so that i will mark you as brainliest ​

Answer 1

ᴀɴsᴡᴇʀ :

Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠ AOC.

To prove : OQ is the bisector of ∠ BOD

Proof :

AB, CD and PQ are straight lines which intersect in O.

∠ AOP = ∠ BOQ (vertically opposite angles)

∠ COP = ∠ DOQ (vertically opposite angles)

∠ AOP = ∠ COP (OP is the bisector of ∠ AOC)

∴ ∠ BOQ = ∠ DOQ

Thus, the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Similarly, the bisector of ∠ AOD also bisects the ∠ BOC.

ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ :

ʜᴏᴘᴇ ɪᴛ ᴡɪʟʟ ʜᴇʟᴘs ʏᴏᴜ ❤️✨

Answer 2

Answer:

Here is the answer in the attachment. HOPE it helps you!