Tavi - Ganatleba

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I Tavi
g
g
amocana 1
mocemulia ∆ABC da ∆A 1 B 1 C 1 , amasTan AB:A 1 B 1 = BC:B 1 C 1 = AC:A 1 C 1 .
ipoveT B kuTxis gradusuli zoma, Tu ∠A 1 =45° da ∠C 1 =70°.
amoxsna:
savarjiSoebi
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ganvixiloT ∆A 1 B 1 C 1 . ∠B 1 =180°-(45°+70°)=65°.
∆ABC~∆A 1 B 1 C 1 (samkuTxedebis msgavsebis III niSnis Tanaxmad).
e.i. ∠B 1 =∠B=65°.
pasuxi: ∠B=65°.
daadgineT, msgavsia Tu ara samkuTxedebi, Tu maTi gverdebis sigrZeebia
1 sm, sm, 1,5 sm da 1 sm, 8 sm, 16 sm.
ABC samkuTxedSi Caxazulia kvadrati ise, rom misi ori wvero AC gverdze
mdebareobs, danarCeni ori ki AB da BC gverdebze. ipoveT kvadratis
gverdis sigrZe, Tu AC=4 sm, xolo AC gverdze daSvebuli simaRlis
sigrZe ki 1 sm-ia.
ABCD paralelogramSi AB=4 0 sm. BC gverdze aRebulia E wertili ise,
rom BE:EC=5:7 da gavlebulia DE wrfe, romelic AB–s gagrZelebas F
wertilSi kveTs. ipoveT BF-is sigrZe.
F wertili ABCD paralelogramis AB gverdis gagrZelebaze Zevs; DF da
AC ikveTeba E wertilSi. ipoveT BF-is sigrZe, Tu AE:EC=m:n da AB=a.
trapeciis fuZeebis sigrZeebi 2sm da 6sm-ia. rogori SefardebiT gayofs
trapeciis simaRles diagonalebis gadakveTis wertilze gavlebuli
fuZeebis paraleluri wrfe?
daamtkiceT, rom trapeciaSi diagonalebiT Seqmnili fuZeebTan mdebare
samkuTxedebi msgavsia.
B C
A D B
ABCD kvadratis sigrZea 5 sm.
AD gverdis gagrZelebaze gadadebulia
DE=BD sigrZis monakveTi. ipoveT S ∆BDE .