which of the following is a regular polygon a. rectangle b.square c. rhombus d. paralellogram
Answers
Answer:
Thus, a square is a regular polygon. c) A parallelogram is the general name for a four-sided polygon where the sides and angles are not all equal.
________________________________
Qᴜᴇsᴛɪᴏɴ:
Wʜɪᴄʜ ᴏғ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ ɪs ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ?
ᴀ) Rᴇᴄᴛᴀɴɢʟᴇ.
ʙ) Sϙᴜᴀʀᴇ.
ᴄ) Pᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ.
ᴅ) Rʜᴏᴍʙᴜs.
Pᴏʟʏɢᴏɴs:
A ᴘᴏʟʏɢᴏɴ ɪs ᴀ sʜᴀᴘᴇ ɪɴ ᴛᴡᴏ ᴅɪᴍᴇɴsɪᴏɴs. Iɴ ᴏʀᴅᴇʀ ғᴏʀ ɪᴛ ᴛᴏ ʙᴇ ᴛʜɪs ᴋɪɴᴅ ᴏғ sʜᴀᴘᴇ, ɪᴛ ɴᴇᴇᴅs ᴛᴏ ʜᴀᴠᴇ ᴀᴛ ʟᴇᴀsᴛ ᴛʜʀᴇᴇ sᴛʀᴀɪɢʜᴛ sɪᴅᴇs ᴄᴏɴɴᴇᴄᴛᴇᴅ ʙʏ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs. Oᴛʜᴇʀᴡɪsᴇ, ɪᴛ ᴡᴏᴜʟᴅ ɴᴏᴛ ʙᴇ ᴀ ᴄʟᴏsᴇᴅ ғɪɢᴜʀᴇ. Tʜɪs ᴍᴇᴀɴs ᴛʜᴀᴛ ᴄᴏᴍᴍᴏɴ sʜᴀᴘᴇs ʟɪᴋᴇ ᴛʀɪᴀɴɢʟᴇs ᴀɴᴅ ʀᴇᴄᴛᴀɴɢʟᴇs ᴀʀᴇ ᴘᴏʟʏɢᴏɴs, ʙᴜᴛ ᴄɪʀᴄʟᴇs, ᴀs ᴛʜᴇʏ ʜᴀᴠᴇ ɴᴏ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇs, ᴀʀᴇ ɴᴏᴛ.
Aɴsᴡᴇʀ ᴀɴᴅ Exᴘʟᴀɴᴀᴛɪᴏɴ:
Aʟʟ ғᴏᴜʀ ᴏғ ᴛʜᴇ sʜᴀᴘᴇs ɢɪᴠᴇɴ ᴀʀᴇ ᴘᴏʟʏɢᴏɴs, ᴀs ᴛʜᴇʏ ᴄᴏɴᴛᴀɪɴ ғᴏᴜʀ ᴄᴏɴɴᴇᴄᴛᴇᴅ sɪᴅᴇs ᴀɴᴅ ᴀʀᴇ ᴄʟᴏsᴇᴅ. Hᴏᴡᴇᴠᴇʀ, ᴡᴇ ᴡᴀɴᴛ ᴛᴏ ᴍᴀᴋᴇ ᴀ sᴛʀᴏɴɢᴇʀ ᴄʟᴀssɪғɪᴄᴀᴛɪᴏɴ, ᴅᴇᴛᴇʀᴍɪɴɪɴɢ ᴡʜᴇᴛʜᴇʀ ᴏʀ ɴᴏᴛ ᴀɴʏ ᴏғ ᴛʜᴇsᴇ ᴀʀᴇ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴs.Rᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴs ʜᴀᴠᴇ sᴛʀᴏɴɢ sʏᴍᴍᴇᴛʀʏ, ᴀs ᴛʜᴇ ʟᴇɴɢᴛʜs ᴏғ ᴀʟʟ ᴏғ ᴛʜᴇ sɪᴅᴇs ᴀɴᴅ ᴛʜᴇ ᴍᴀɢɴɪᴛᴜᴅᴇs ᴏғ ᴀʟʟ ᴏғ ᴛʜᴇ ᴀɴɢʟᴇs ᴀʀᴇ ᴇϙᴜᴀʟ.
ᴀ) A ʀᴇᴄᴛᴀɴɢʟᴇ ʜᴀs ғᴏᴜʀ ɴɪɴᴇᴛʏ ᴅᴇɢʀᴇᴇ ᴀɴɢʟᴇs, ʙᴜᴛ ᴛʜᴇ sɪᴅᴇs ᴀʀᴇ ɴᴏᴛ ᴀʟʟ ɢᴜᴀʀᴀɴᴛᴇᴇᴅ ᴛᴏ ʙᴇ ᴇϙᴜᴀʟ. Tʜɪs ɪs ʙᴇᴄᴀᴜsᴇ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ᴄᴀɴ ʙᴇ ʟᴏɴɢᴇʀ ᴛʜᴀɴ ɪᴛ ɪs ᴡɪᴅᴇ ᴏʀ ᴡɪᴅᴇʀ ᴛʜᴀɴ ɪᴛ ɪs ʟᴏɴɢ. Iᴛ ᴄᴏᴜʟᴅ ᴀʟsᴏ ʙᴇ ᴀs ᴡɪᴅᴇ ᴀs ɪᴛ ɪs ʟᴏɴɢ, ᴡʜɪᴄʜ ɪs ᴀ sᴘᴇᴄɪғɪᴄ ᴄᴀsᴇ ᴛʜᴀᴛ ᴛᴜʀɴs ᴛʜɪs ʀᴇᴄᴛᴀɴɢʟᴇ ɪɴᴛᴏ ᴀ sϙᴜᴀʀᴇ. Iɴ ᴛʜɪs ᴄᴀsᴇ, ᴀɴᴅ ᴏɴʟʏ ɪɴ ᴛʜɪs ᴄᴀsᴇ, ɪs ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ. Oᴛʜᴇʀᴡɪsᴇ, ɪᴛ ɪs ɴᴏᴛ.
ʙ) A sϙᴜᴀʀᴇ ʜᴀs ғᴏᴜʀ ɴɪɴᴇᴛʏ ᴅᴇɢʀᴇᴇ ᴀɴɢʟᴇs ᴀs ᴡᴇʟʟ, ʙᴜᴛ ᴛʜɪs ᴛɪᴍᴇ, ᴀʟʟ ғᴏᴜʀ sɪᴅᴇ ʟᴇɴɢᴛʜs ᴀʀᴇ ʀᴇϙᴜɪʀᴇᴅ ᴛᴏ ʙᴇ ᴇϙᴜᴀʟ. Tʜᴜs, ᴀ sϙᴜᴀʀᴇ ɪs ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ.
ᴄ) A ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ɪs ᴛʜᴇ ɢᴇɴᴇʀᴀʟ ɴᴀᴍᴇ ғᴏʀ ᴀ ғᴏᴜʀ-sɪᴅᴇᴅ ᴘᴏʟʏɢᴏɴ ᴡʜᴇʀᴇ ᴛʜᴇ sɪᴅᴇs ᴀɴᴅ ᴀɴɢʟᴇs ᴀʀᴇ ɴᴏᴛ ᴀʟʟ ᴇϙᴜᴀʟ. Wᴇ ʜᴀᴠᴇ ᴛᴡᴏ ᴘᴀɪʀs ᴏғ ᴇϙᴜᴀʟ sɪᴅᴇs, ʟɪᴋᴇ ᴛʜᴇ ᴄᴀsᴇ ᴡɪᴛʜ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ, ᴀɴᴅ ᴛᴡᴏ ᴘᴀɪʀs ᴏғ ᴇϙᴜᴀʟ ᴀɴɢʟᴇs, ʟɪᴋᴇ ᴛʜᴇ ᴄᴀsᴇ ᴡɪᴛʜ ᴀ ʀʜᴏᴍʙᴜs. As ɪs ᴛʜᴇ ᴄᴀsᴇ ᴡɪᴛʜ ᴛʜᴇ ᴏᴛʜᴇʀ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟs ᴅɪsᴄᴜssᴇᴅ ɪɴ ᴛʜɪs ᴘʀᴏʙʟᴇᴍ, ᴀ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ᴄᴏᴜʟᴅ ʙᴇ ᴀ sϙᴜᴀʀᴇ ɪғ ᴀʟʟ ᴏғ ᴛʜᴇ ᴀɴɢʟᴇs ᴀɴᴅ sɪᴅᴇ ʟᴇɴɢᴛʜs ᴀʀᴇ ᴇϙᴜᴀʟ. Hᴏᴡᴇᴠᴇʀ, ɪғ ᴛʜᴇʏ ᴀʀᴇ ɴᴏᴛ, ᴛʜᴇɴ ɪᴛ ɪs ɴᴏᴛ ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ.
ᴅ) A ʀʜᴏᴍʙᴜs ʜᴀs ғᴏᴜʀ ᴇϙᴜᴀʟ sɪᴅᴇ ʟᴇɴɢᴛʜs. Hᴏᴡᴇᴠᴇʀ, ɪᴛs ᴀɴɢʟᴇs ᴀʀᴇ ɴᴏᴛ ᴜsᴜᴀʟʟʏ ᴇϙᴜᴀʟ. Iɴ ᴍᴏsᴛ ᴄᴀsᴇs, ᴛᴡᴏ ᴀɴɢʟᴇs ᴀʀᴇ ɢʀᴇᴀᴛᴇʀ ᴛʜᴀɴ ɴɪɴᴇᴛʏ ᴅᴇɢʀᴇᴇs ᴀɴᴅ ᴛᴡᴏ ᴀɴɢʟᴇs ᴀʀᴇ ʟᴇss ᴛʜᴀɴ ɴɪɴᴇᴛʏ ᴅᴇɢʀᴇᴇs. Hᴏᴡᴇᴠᴇʀ, ʟɪᴋᴇ ᴛʜᴇ ᴄᴀsᴇ ᴡɪᴛʜ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ, ᴛʜᴇʀᴇ ɪs ᴀ sᴘᴇᴄɪғɪᴄ ᴄᴀsᴇ ᴡʜᴇʀᴇ ᴛʜᴇ ᴀɴɢʟᴇs ᴀʀᴇ ᴀʟʟ ᴇϙᴜᴀʟ, ᴡʜɪᴄʜ ᴛᴜʀɴs ɪᴛ ɪɴᴛᴏ ᴀ sϙᴜᴀʀᴇ ᴀɢᴀɪɴ. Lɪᴋᴇ ʙᴇғᴏʀᴇ, ɪɴ ᴛʜɪs ᴄᴀsᴇ, ᴀɴᴅ ᴏɴʟʏ ɪɴ ᴛʜɪs ᴄᴀsᴇ, ɪs ᴀ ʀʜᴏᴍʙᴜs ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ. Oᴛʜᴇʀᴡɪsᴇ ɪᴛ ɪs ɴᴏᴛ.
Tʜᴇ ᴏɴʟʏ sʜᴀᴘᴇ ᴛʜᴀᴛ ɪs ɢᴜᴀʀᴀɴᴛᴇᴇᴅ ᴛᴏ ʙᴇ ᴀ ʀᴇɢᴜʟᴀʀ ᴘᴏʟʏɢᴏɴ ɪs ʙ) Sϙᴜᴀʀᴇ.
Aɴs- (ʙ) Sϙᴜᴀʀᴇ
________________________________