How kuwana pakakwirira trapezoid?

In hwedu kazhinji tinofanira kubata nokushandiswa geometry mune tsika, akadai kuvakwa. Pakati rakajairika geometric zvitarisiko, pane trapeze. Uye kuti ave nechokwadi kuti basa racho rakabudirira uye akanaka, unofanira zvakakodzera uye yakarurama kukarukureta ose okunze kuti munhu akadaro.

Chii chinonzi dombo rinokosha? Izvi quadrilateral convex ine mbiri dzakafanana mativi, anonzi mujinga trapezoid. Asi pane zvimwe zviviri kuti batanidza chikonzero izvi. Dzinonzi lateral. Imwe nyaya chokuita nhamba iyi, ndiyo: "Sei kuwana kukwirira trapezoid" Just vanofanira kuteerera kureba - a chidimbu kuti anosarudza daro kubva napamaruva mumwe. Pane nzira dzakawanda kuti aone kure ichi, zvichienderana pamusoro anozivikanwa variables.

1. Dzinozivikanwa kwazvo vose bwezvingoro, b kureva navo uye K, uyewo nzvimbo yacho trapezoid. Kushandisa anozivikanwa tsika kuwana kukwirira trapezoid, muchiitiko ichi nyore. Sezvo anozivikanwa kubva geometry, kuti trapezoid nzvimbo rinowanikwa sezvo zvibereko hafu Verengai nechigadziko uye kukwirira. Kubva fomura izvi vanogona zvinodiwa ukoshi nyore. Kuti aite izvi, kugovera nzvimbo iri hafu uwandu chikonzero. Muna yemaitiro taitsvaka seizvi:

S = ((b + k) / 2) * H, pano H = S / ((b + k) / 2) = 2 * S / (b + k)

2. Dzinozivikanwa kureba midline, isu anoratidza D, uye dzakaenzana. Nokuti vaya vasingazivi, pakati mutsetse uri chinhambwe pakati midpoints ari kumativi. How kuwana kukwirira trapezoid iyi? Maererano pfuma trapezoid, pakati mutsetse anoenderana hafu uwandu bwezvingoro, i.e. D = (b + k) / 2. Zvakare isu kushandisa fomura dzakaenzana. Pavanotsiva hafu chitsama hwaro pamusoro kukosha pakati mutsetse, tinowana zvinotevera:

S = D * bare

Sezvinogona kuoneka kubva nzira akawana chaizvo nyore vaziva kukwirira. Kugovera nzvimbo pamusoro midline kunokosha, tinozowana zvisingazivikanwi uwandu. Tinonyora fomura ichi:

H = S / D

3. Dzinozivikanwa pakureba rumwe rutivi (b), kundosvikazve pakona aumba pakati rweseri uye chikuru chawo. Mhinduro kumubvunzo sei kuwana kukwirira trapezoid, ndiyewo panyaya iyi. Funga trapezoid ABCD, apo AB uye CD ndivo lateral mativi, sezvamakaropafadzwa AB = b. Kudeuka chawo ndiyo AD. The angled inoumbwa AB uye AD runotaurwa α. Kubva nguva B dzinosiya nokukwirira ekurwisana pamusoro AD chawo. Zvino funga kunoguma Triangle ABF, inova rectangular. Side AB ndiye hypotenuse, uye BF-gumbo. Kubva pfuma rworudyi, triangle reshiyo ukoshi cathetus uye hypotenuse unoenderana kukosha Sine pakati rekona nevakomana cathetus (BF). Naizvozvo, kufunga pamusoro apa, kuverenga kureba trapezoid vawande kukosha imwe chinoitwa uye Sine pakati pakona α. Mune nzira iri sezvinotevera:

H = B * chivi (α)

4. Saizvozvowo, nyaya kana anozivikanwa kukura divi uye rekona runotaurwa β, kuumbwa pakati rweseri nechigadziko duku. Pakugadzirisa dambudziko rakadai, pakona pakati parutivi chinozivikanwa kukwirira uye ndakaiswa 90 ° - β. Kubva ehupfumi pakati zvokuridza - reshiyo urefu cathetus uye hypotenuse rinoenderana cosine pakati rekona rakamiswa pakati pavo. Kubva mutoo uyu zviri nyore kuona kukwirira ukoshi:

H = B * Kosi (β-90 °)

5. kuwana kukwirira trapezoid, kana kuzivikanwa chete kuti nharaunda yacho yakanyorwa denderedzwa? Kubva tsanangudzo denderedzwa, nezvezvitadzo imwe pfungwa nechimwe. Uyezve, pfungwa idzi zvichienderana ne nepakati denderedzwa. Kubva ichi zvinoreva kuti daro pakati pavo ndiye dhayamita, uye panguva imwecheteyo, pakakwirira trapezoid. Zvinoita seizvi:

H = 2 * R

6. Kazhinji pane mabasa kuti vanofanira kuwana kureba ane isosceles trapezoid. Yeuka kuti imwe trapezoid zvakaenzana mativi anonzi isosceles. How kuwana kukwirira isosceles trapezoid? Kana diagonals vari perpendicular yakakwirira akaenzana hafu mubatanidzwa pezvingoro.

Asi zvokuita kana diagonals vasiri perpendicular? Funga isosceles trapezoid ABCD. Maererano ehupfumi ayo, zvigadziko zvinofanana. Kubva ichi zvinoreva kuti pamakona mujinga achava vakaenzana. Swederai maviri dzakakwirira BF uye CM. Pachishandiswa zvataurwa, zvinganzi vakati zvokuridza ABF uye DCM vakaenzana, kureva, AF = DM = (AD - BC) / 2 = (Bk) / 2. Zvino, inobva ezvinhu dambudziko, havatsananguri anozivikanwa kwazvo, uye ipapo wana kukwira, kufungisisa zvose ehupfumi ane isosceles trapezoid.