Question

state and prove thales Theorem.​

Answer 1

Answer:

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

Answer 2

sᴛᴀᴛᴇᴍᴇɴᴛ: ɪғ ᴀ ʟɪɴᴇ ɪs ᴅʀᴀᴡɴ ᴘᴀʀᴀʟʟᴇʟ ᴛᴏ ᴏɴᴇ sɪᴅᴇ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ, ᴛᴏ ɪɴᴛᴇʀᴇsᴛ ᴛʜᴇ ᴏᴛʜᴇʀ ᴛᴡᴏ sɪᴅᴇs ᴀᴛ ɪɴᴅɪsᴛɪɴᴄᴛ ᴘᴏɪɴᴛs, ᴛʜᴇ ᴏᴛʜᴇʀ ᴛᴡᴏ sɪᴅᴇs ᴀʀᴇ ᴅɪᴠɪᴅᴇᴅ ɪɴ ᴛʜᴇ sᴀᴍᴇ ʀᴀᴛɪᴏ.

From Diagram....

ɢɪᴠᴇɴ: - ɪɴ △ᴀʙᴄ,ᴅᴇ∥ʙᴄ

ᴛᴏ ᴘʀᴏᴠᴇ:- ᴀᴅ/ᴅʙ = ᴀᴇ/ᴇᴄ

ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ:- ʙᴇ ᴀɴᴅ ᴄᴅ ᴀʀᴇ ᴊᴏɪɴᴇᴅ. ᴇғ⊥ᴀʙ ᴀɴᴅ ᴅɴ⊥ᴀʟ

ᴀʀᴇ ᴅʀᴀᴡɴ.

ᴘʀᴏᴏғ:-

ᴀʀ(△ᴀᴅᴇ) = 1/2×ᴀᴅ×ᴇғ

=1/2×ᴀᴇ×ᴅɴ

ᴀʀ(△ʙᴅᴇ) = 1/2×ʙᴅ×ᴇғ

ᴀʀ(△ᴄᴅᴇ) = 1/2×ᴇᴄ×ᴅɴ

ᴀʀ(△ᴀᴅᴇ)/ᴀʀ(△ʙᴅᴇ) = 1/2×ᴀᴅ×ᴇғ/1/2×ʙᴅ×ᴇғ ........(1)

ᴀʀ(△ᴀᴅᴇ)/ᴀʀ(△ᴄᴅᴇ) = 1/2×ᴀᴇ×ᴅɴ/1/2×ᴇᴄ×ᴅɴ ........(2)

ʙᴜᴛ, ᴀʀ(△ʙᴅᴇ) = ᴀʀ(△ᴄᴅᴇ) ..............(3)

ᴀs ᴛʜᴇʏ ᴀʀᴇ ᴏɴ ᴛʜᴇ sᴀᴍᴇ ʙᴀsᴇ ᴅᴇ ᴀɴᴅ ᴅᴇ∥ʙᴄ

ғʀᴏᴍ (1), (2) ᴀɴᴅ (3) ᴡᴇ ɢᴇᴛ ᴀᴅ/ᴅʙ = ᴀᴇ/ᴇᴄ