maTematika 7

12. monakveTis SuamarTobireziume:moswavlem unda SeZlos monakveTis boloebidan Tanabrad daSorebul wertilTa geometriuliadgilis ageba. monakveTis SuamarTobis ganmarteba, misi Tvisebebis Camoyalibeba.mocemuli winadadebis Sebrunebuli winadadebis Camoyalibeba da imis Semowmeba,aris Tu ara Sebrunebuli winadadeba WeSmariti.amoxsnebi, miTiTebebi:2. AC=BC=5B3. moc.: ∆ABCBM=MCMD⊥BCBD=5sm, AC=8,5sm.Mu.v. AD da DCADCMD BC monakveTis SuamarTobia, e.i. DC=BD=5; AD=8,5–5=3.4. moc.: AM=MB; AN=NCMD⊥AB DN⊥BCAu.d. a) BD=DC; b) ∠A=∠B+∠CMNa) MDAB-s SuamarTobia, amitom DB=DA;ND BC-s SuamarTobia, e.i. DA=DC.BDmiviReT DB=DA=DC, e.i. BD=DC.b) ∆ADB tolferdaa,e.i. ∠BAD=∠B, analogiurad ∆ADC-Si ∠DAC=∠C.∠BAC=∠BAD+∠DAC=∠B+∠C, r.d.g.5. ganv. ∆ABK da ∆CBKAB=BC; AK=KCBC∠BAK=∠BAM+∠MAK=∠MCK+∠BCM=∠BCK ⇒⇒ samkuTxedebi tolia I niSnis Tanaxmad,e.i. ∠ABM=∠CBM,miviReT BM ABC kuTxis biseqtrisaa,amitom BM simaRlecaa da medianac, e.i. BK AC-sSuamarTobia.AMKC6. 10a+b=72+a+b, saidanac a=8. e.i. aseTi orniSna ricxvebia yvela is ricxvebi, romelTaaTeulebis cifria 8. 80; 81; 82;... 89.7. WeSmaritia C⊂B⊂A g)nebismieri tolgverda aris tolferdac, xolo tolferda samkuTxedi kisamkuTxedis kerZo saxea.94masc_cigni_VII_kl_cor.indd 94 03.07.2012 15:46:55