Question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that
CAD=CBD​

Answer 1

Answer:-

➡️AC ɪs ᴛʜᴇ ᴄᴏᴍᴍᴏɴ ʜʏᴘᴏᴛᴇɴᴜsᴇ. ∠B=∠D=90°.

➡️Tᴏ ᴘʀᴏᴠᴇ,

➡️∠CAD=∠CBD

Pʀᴏᴏғ:

➡️Sɪɴᴄᴇ, ∠ABC ᴀɴᴅ ∠ADC ᴀʀᴇ 90°. 

➡️Tʜᴇsᴇ ᴀɴɢʟᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ sᴇᴍɪ-ᴄɪʀᴄʟᴇ. 

➡️Tʜᴜs, ʙᴏᴛʜ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ ʟʏɪɴɢ ɪɴ ᴛʜᴇ sᴇᴍɪ-ᴄɪʀᴄʟᴇ ᴀɴᴅ AC ɪs ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ.

⇒ Pᴏɪɴᴛs A,B,C ᴀɴᴅ D ᴀʀᴇ ᴄᴏɴᴄʏᴄʟɪᴄ.

➡️Tʜᴜs, CD ɪs ᴛʜᴇ ᴄʜᴏʀᴅ.

⇒∠CAD=∠CBD        ...Aɴɢʟᴇs ɪɴ ᴛʜᴇ sᴀᴍᴇ sᴇɢᴍᴇɴᴛ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ

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Answer 2

Step-by-step explanation:

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