Question

abcd is a quadrilateral in which all 4 sides are equal . show taht both pairs opposite sides are parallel​

Answer 1

Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-

ABCD ɪs ᴀ Qᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ Wɪᴛʜ Fᴏᴜʀ Eǫᴜᴀʟ Sɪᴅᴇs

Iғ Tʜᴇ Sɪᴅᴇs Aʀᴇ Eǫᴜᴀʟ Tʜᴇʏ Wɪʟʟ Pʀᴏᴅᴜᴄᴇ Fᴏᴜʀ Eǫᴜᴀʟ Aɴɢʟᴇs

Hᴇɴᴄᴇ, Eᴀᴄʜ Aɴɢʟᴇ Wɪʟʟ ʙᴇ 90° ( Sᴜᴍ ᴏғ Iɴᴛᴇʀɪᴏʀ Aɴɢʟᴇs ɪs 360° )

Hᴇɴᴄᴇ, ABCD ɪs Cᴏɴsɪᴅᴇʀᴇᴅ ᴀs ᴀ 'Sǫᴜᴀʀᴇ'

AC Aɴᴅ BD Aʀᴇ Jᴏɪɴᴇᴅ Wʜɪᴄʜ Mᴇᴇᴛ ᴀᴛ O

AC Aɴᴅ BD Aʀᴇ Dɪᴀɢᴏɴᴀʟs Wʜɪᴄʜ Bɪsᴇᴄᴛ Iɴᴛᴇʀɪᴏʀ Aɴɢʟᴇs.

Aɴɢʟᴇ BAD ɪs Bɪsᴇᴄᴛᴇᴅ ʙʏ AC

Aɴɢʟᴇs BAC = DAC

Aɴɢʟᴇ BCD ɪs Bɪsᴇᴄᴛᴇᴅ ʙʏ AC

Aɴɢʟᴇs ACD = BCA

Sɪɴᴄᴇ, BAD = BCD = 90°

Aɴɢʟᴇs BAC = DAC = Aɴɢʟᴇs ACD = BCA

BAC = ACD

Tʜᴇʏ Aʀᴇ Aʟsᴏ Iɴᴛᴇʀɪᴏʀʟʏ Aʟᴛᴇʀɴᴀᴛᴇ ᴛᴏ Eᴀᴄʜ Oᴛʜᴇʀ.

Sᴏ ʙʏ Cᴏɴᴠᴇʀsᴇ Tʜᴇᴏʀᴀᴍ,

AB ɪs Pᴀʀᴀʟʟᴇʟ ᴛᴏ CD

Sɪᴍɪʟᴀʀʟʏ, Aɴɢʟᴇs ABD = CBD = ADB = CDB ( Wʜᴇɴ BD ɪs Tʜᴇ Bɪsᴇᴄᴛᴏʀ )

CBD = ADB

Tʜᴇʏ Aʀᴇ Aʟsᴏ Iɴᴛᴇʀɪᴏʀʟʏ Aʟᴛᴇʀɴᴀᴛᴇ ᴛᴏ Eᴀᴄʜ Oᴛʜᴇʀ.

Sᴏ ʙʏ Cᴏɴᴠᴇʀsᴇ Tʜᴇᴏʀᴀᴍ,

AD ɪs Pᴀʀᴀʟʟᴇʟ ᴛᴏ BC

Hᴇɴᴄᴇ Oᴘᴘᴏsɪᴛᴇ Pᴀɪʀs ᴏғ Sɪᴅᴇs Aʀᴇ Pᴀʀᴀʟʟᴇʟ ᴛᴏ Eᴀᴄʜ Oᴛʜᴇʀ.

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