∞’ §˘Î›Ԣ – ∂ÁÁÂÁÚ·Ì̤ӷ ÙÂÙÚ¿Ï¢ڷ ñ ™ÂÏ›‰· 35
∞’ ∆¿ÍË – ∂ÁÁÂÁÚ·Ì̤ӷ ÙÂÙÚ¿Ï¢ڷ
1 ¢Ú·ÛÙËÚÈfiÙËÙ·
ÃÚfiÓÔ˜: 1 ‰È‰·ÎÙÈ΋ ÒÚ·
¢Ú·ÛÙËÚÈfiÙËÙ·
™Ùfi¯Ô˜
∏ ‰ÈÂÚ‡ÓËÛË ÙˆÓ ‚·ÛÈÎÒÓ È‰ÈÔÙ‹ÙˆÓ ÙˆÓ ÂÁÁÂÁÚ·ÌÌ¤ÓˆÓ ÙÂÙÚ·χڈÓ. ∏ ¢ı›·
ÙÔ˘ Simson.
∫·Ù·Û΢‹
ñ ∫·Ù·Û΢¿ÛÙ ·ÎÏÔ Ì ΤÓÙÚÔ O.
ñ ∫·Ù·Û΢¿ÛÙ ¤Ó· ÙÚ›ÁˆÓÔ ∞µ° Î·È ÙȘ Ï¢ڤ˜ ÙÔ˘ ∞µ, µ° Î·È ∞°, ηÈ
¯ÚˆÌ·Ù›ÛÙ ÙȘ ÌÔ‚.
ñ ∫·Ù·Û΢¿ÛÙ ‰‡Ô ¢ı›˜ Â1 Î·È Â2, Ô˘ Ó· ‰È¤Ú¯ÔÓÙ·È Ù· ÛËÌ›· µ, ° ηÈ
∞, °, ·ÓÙ›ÛÙÔȯ·.
ñ ∫·Ù·Û΢¿ÛÙ ¤Ó· Ù˘¯·›Ô ÛËÌÂ›Ô ∂ ¿Óˆ ÛÙÔÓ Î‡ÎÏÔ Ì ΤÓÙÚÔ O.
ñ ∫·Ù·Û΢¿ÛÙ ÙȘ οıÂÙ˜ ¢ı›˜ ·fi ÙÔ ∂ ÛÙȘ Â1, Â2 Î·È ∞µ, Î·È ÔÓÔÌ¿ÛÙ ÙȘ ˙1, ˙2 Î·È ˙3, ·ÓÙ›ÛÙÔȯ·.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ ÛËÌÂ›Ô ÙÔÌ‹˜ Ù˘ ¢ı›·˜ ˙1 Ì ÙËÓ Â˘ı›· Â1, Î·È ÔÓÔÌ¿ÛÙ ÙÔ ¢.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ Â˘ı‡ÁÚ·ÌÌÔ ÙÌ‹Ì· ∂¢.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ ÛËÌÂ›Ô ÙÔÌ‹˜ Ù˘ ¢ı›·˜ ˙2 Ì ÙËÓ Â˘ı›· Â2, Î·È ÔÓÔÌ¿ÛÙ ÙÔ ∑.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ Â˘ı‡ÁÚ·ÌÌÔ ÙÌ‹Ì· ∂∑.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ ÛËÌÂ›Ô ÙÔÌ‹˜ Ù˘ ¢ı›·˜ ˙3 Ì ÙÔ Â˘ı‡ÁÚ·ÌÌÔ ÙÌ‹Ì· ∞µ,
Î·È ÔÓÔÌ¿ÛÙ ÙÔ ∫.
ñ ∫·Ù·Û΢¿ÛÙ ÙÔ Â˘ı‡ÁÚ·ÌÌÔ ÙÌ‹Ì· ∂∫. Ãڈ̷ٛÛÙ ÎfiÎÎÈÓ· Ù· ¢ı‡ÁÚ·ÌÌ· ÙÌ‹Ì·Ù· ∂¢, ∂∑ Î·È ∂∫, ˙1, ˙2 Î·È ˙3. ∞ÔÎÚ‡„Ù ÙȘ ¢ı›˜ ˙1, ˙2
Î·È ˙3.
™¯‹Ì· §_12
¢Ú·ÛÙËÚÈfiÙËÙ˜ ÁˆÌÂÙÚ›·˜ ÛÙÔ ÂÚÈ‚¿ÏÏÔÓ Cabri – geometry II ñ
™ÂÏ›‰· 36 ñ ∞’ §˘Î›Ԣ – ∂ÁÁÂÁÚ·Ì̤ӷ ÙÂÙÚ¿Ï¢ڷ
ñ ∫·Ù·Û΢¿ÛÙ ٷ ¢ı‡ÁÚ·ÌÌ· ÙÌ‹Ì·Ù· ¢∫ Î·È ∫∑.
ñ ∫·Ù·Û΢¿ÛÙ ÙË ÁˆÓ›· ¢∫∑, ÔÓÔÌ¿ÛÙ ÙËÓ ∫2 Î·È ÌÂÙÚ‹ÛÙ ÙËÓ ·˘ÙfiÌ·Ù·.
¢ÈÂÚ‡ÓËÛË
ªÂÙ·ÎÈÓ‹ÛÙ ÙÔ ÛËÌÂ›Ô ∂ ÛÙËÓ ÂÚÈʤÚÂÈ· ÙÔ˘ ·ÎÏÔ˘ ΤÓÙÚÔ˘ O ‹ / Î·È Ù· ÛËÌ›·
∞, µ Î·È °.
1. ¶ÔÈ· ˘fiıÂÛË ÌÔÚ›Ù ӷ ‰È·Ù˘ÒÛÂÙ ÁÈ· ÙË ı¤ÛË ÙˆÓ ÛËÌ›ˆÓ ¢, ∫ Î·È ∑;
¢È·Ù‡ˆÛË ˘fiıÂÛ˘
∂‰Ò ·Ó·Ì¤ÓÂÙ ÔÈ Ì·ıËÙ¤˜ Ó· ‰È·Ù˘ÒÛÔ˘Ó ÙËÓ ˘fiıÂÛË fiÙÈ Ù· ÛËÌ›· ¢, ∫ Î·È ∑
Â›Ó·È ¿ÓÙÔÙÂ Û˘Ó¢ıÂȷο.
2. ªÔÚ›Ù ӷ ·ÈÙÈÔÏÔÁ‹ÛÂÙ ÙËÓ ·¿ÓÙËÛ‹ Û·˜;
∞ÈÙÈÔÏfiÁËÛË
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™ÙËÓ ÂÚ›ÙˆÛË Ô˘ ÔÈ Ì·ıËÙ¤˜ ‰ÂÓ ÌÔÚÔ‡Ó Ó· ·ÈÙÈÔÏÔÁ‹ÛÔ˘Ó ÙËÓ ·¿ÓÙËÛ‹ ÙÔ˘˜,
ÙÔ˘˜ ηϛ٠ӷ ÂÈϤÍÔ˘Ó Î·È Ó· ÌÂÙÚ‹ÛÔ˘Ó ÙȘ ÁˆÓ›Â˜ ∞∑∂=∑, ∂∫∞=∫1 ηÈ
∂¢µ=¢1. ™ÙË Û˘Ó¤¯ÂÈ·, ÙÔ˘˜ οÓÂÙ ÙËÓ ·ÎfiÏÔ˘ıË ÂÚÒÙËÛË:
ªÂ ‚¿ÛË Ù· ‰Â‰Ô̤ӷ ÙÔ˘ Û¯‹Ì·Ùfi˜ Û·˜, ÌÂÏÂÙ‹ÛÙ ٷ ÙÂÙÚ¿Ï¢ڷ ∂∫∑∞ ηÈ
∂∫µ¢. ¶ÔÈÔ Â›Ó·È ÙÔ Â›‰Ô˜ ÙˆÓ ÙÂÙÚ·ÏÂ‡ÚˆÓ ·˘ÙÒÓ;
∞¿ÓÙËÛË
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ñ ¢Ú·ÛÙËÚÈfiÙËÙ˜ ÁˆÌÂÙÚ›·˜ ÛÙÔ ÂÚÈ‚¿ÏÏÔÓ Cabri – geometry II