Nchikota nke akụkụ nke a triangle. The Theorem na nchikota nke akụkụ nke a triangle

The triangle bụ a polygon enwe atọ n'akụkụ (atọ akụkụ). Ọtụtụ mgbe, ndị akụkụ denoted site obere akwụkwọ ozi kwekọrọ ekwekọ isi obodo leta, nke na-anọchi anya na-abụghị vertices. N'isiokwu a anyị na-a lee anya na ndị a na ụdị geometric shapes, Theorem, nke akowa ihe bụ hà nchikota nke akụkụ nke a triangle.

Ụdị kasị akụkụ

Ndị na-esonụ ụdị nke polygon na atọ vertices:

• nnukwu-angled, nke niile akụkụ ndị nkọ;
• akụkụ anọ enwe otu nri n'akuku, n'akụkụ akpụ ya, zoro aka ụkwụ, n'akụkụ nke na-ewekarị abụghị na nri n'akuku a na-akpọ hypotenuse;
• obtuse mgbe otu n'akuku bụ obtuse ;
• isosceles, onye abụọ n'akụkụ na-hà, na-akpọ ha mpụta, nke atọ - a triangle na a isi;
• equilateral enwe atọ hà n'akụkụ.

Njirimara

Igbunye bụ isi Njirimara na ndị e ji mara nke ọ bụla ụdị triangle:

• abụghị kasị ukwuu n'akụkụ bụ mgbe niile ukwuu n'akuku, na Anglịkan;
• hà akụkụ na ncherita-hà-kasị ọzọ, na Anglịkan;
• na ihe ọ bụla triangle nwere ihe abụọ nnukwu akụkụ;
• elu n'akuku ukwuu karịa ihe ọ bụla esịtidem n'akuku bụghị n'akụkụ thereto;
• nchikota nke abụọ ọ bụla, akụkụ bụ mgbe ihe na-erughị 180 degrees;
• mputa n'akuku nhata nchikota nke abụọ ndị nke ọzọ n'akụkụ, nke na-adịghị mezhuyut na ya.

The Theorem na nchikota nke akụkụ nke a triangle

The Theorem na-ekwu na ọ bụrụ na ị tinye elu niile nkuku nke geometric udi, nke dị na Euclidean ụgbọelu, mgbe ahụ, ha nchikota ga-180 degrees. Ka anyị na-agbalị iji gosi na nke a Theorem.

Ka anyị na-enwe ihe aka ike triangle na vertices KMN. Gafee n'elu nke M ga jide a kpọmkwem ihe yiri ka akara KN (ọbụna a akara na-akpọ Euclid). Ọ ga-kwuru ebe A ka ihe K na A na-ndokwa si dị iche iche n'akụkụ abụọ nke akara MN. Anyị na-enweta otu n'akuku nke AMS na MUF, nke na, dị ka ime, edina crosswise na-etolite intersecting MN na njikọ na kpọmkwem CN na MA, nke bụ yiri. Site na nke a, ọ pụtara na nchikota nke akụkụ nke triangle, emi odude ke vertices nke M na N bụ hà size nke CMA n'akuku. All atọ akụkụ iso nke a nchikota hà nchikota nke akụkụ nke KMA na MCS. Ebe ọ bụ na data bụ esịtidem akụkụ ikwu kwadoro ukem edoghi cl na cm MA na intersecting, ha nchikota bụ 180 degrees. Nke a na-egosi na Theorem.

N'ihi

Nke n'elu n'elu Theorem egosi ndị na-esonụ corollary: ọ bụla triangle nwere ihe abụọ nnukwu angles. Iji gosi na nke a, ka anyị were na a geometrical ọgụgụ nwere naanị otu nnukwu n'akuku. I nwekwara ike iche na ọ dịghị nke nkuku bụ adịghị nkọ. Na nke a ọ ga-abụ na ihe abụọ akụkụ, ịdị ukwuu nke bụ hà ma ọ bụ ukwuu karịa 90 degrees. Ma mgbe ahụ, nchikota nke akụkụ dị ukwuu karịa 180 degrees. Ma, nke a nwere ike ịbụ, dị ka dị ka Theorem nchikota akụkụ nke a triangle bụ hà 180 Celsius - ọzọ, ọ na-erughị. Nke ahụ bụ ihe a ga-egosi.

Property n'èzí nkuku

Gịnị bụ nchikota nke akụkụ nke a triangle, nke bụ mpụga? Azịza nke ajụjụ a pụrụ inweta site n'itinye otu n'ime ụzọ abụọ. Nke mbụ bụ na ị chọrọ ịhụ nchikota nke akụkụ, nke na-e otu na onye ọ bụla vertex, ya bụ, atọ angles. The abụọ na-egosi na ị chọrọ ịhụ nchikota nke isii akụkụ na vertices. Obibi na mmalite nke mbụ n'onwe. N'ihi ya, triangle nwere isii elu nkuku - na elu nke ọ bụla n'ime ihe abụọ ahụ. Ọ bụla ụzọ nwere hà akụkụ n'etiti onwe ha, ebe ọ bụ na ha na-akwụ ọtọ:

∟1 = ∟4, ∟2 = ∟5, ∟3 = ∟6.

Ke adianade do, ọ na-mara na elu akuku nke a triangle nhata nchikota nke abụọ n'ime ime, nke na-adịghị mezhuyutsya na ya. ya mere,

∟1 = ∟A + ∟S, ∟2 = ∟A + ∟V, ∟3 = ∟V + ∟S.

Site na nke a ọ na-egosi na nchikota nke mputa akụkụ, nke na-e otu otu nso bụla vertex ga-hà:

∟1 + ∟2 + ∟3 = ∟A + + ∟S ∟A ∟V + + + ∟V ∟S = 2 x (∟A + ∟V ∟S +).

O bu na nchikota nke akụkụ nhata 180 ogo, ọ nwere ike rụrụ ụka na ∟A + ∟V ∟S = + 180 Celsius. Nke a pụtara na ∟1 + ∟2 + ∟3 = 2 x 180 Celsius = 360 Celsius. Ọ bụrụ na nke abụọ nhọrọ na-eji, na nchikota nke isii akụkụ ga-anata ukwuu ugboro abụọ. Ntụgharị nchikota nke akụkụ nke a triangle n'èzí ga-abụ:

∟1 + ∟2 + ∟3 + ∟4 + ∟5 + ∟6 = 2 x (∟1 + ∟2 + ∟2) = 720 Celsius.

nri triangle

Gịnị bụ hà nchikota nke akụkụ nke a nri triangle, bụ agwaetiti? Azịza ya bụ, ọzọ, si Theorem, nke na-ekwu na akụkụ nke a triangle tinye 180 degrees. A ụda anyị mkwuputa (onwunwe) dị ka ndị a: na a nri triangle nkọ akụkụ tinye ruo 90 degrees. Anyị na-egosi ya n'ịbụ eziokwu. Ka nyere triangle KMN, nke ∟N = 90 Celsius. Ọ dị mkpa iji gosi na ∟K ∟M = + 90 Celsius.

N'ihi ya, dị ka Theorem na nchikota nke akụkụ ∟K + ∟M ∟N + = 180 Celsius. Na ọnọdụ a na ọ bụ kwuru na ∟N = 90 Celsius. Ọ amama ∟K ∟M + + 90 Celsius = 180 Celsius. Nke ahụ bụ ∟K ∟M + = 180 Celsius - 90 Celsius = 90 Celsius. Nke ahụ bụ ihe anyị kwesịrị iji gosi na.

Na mgbakwunye na n'elu Njirimara nke a nri triangle, i nwere ike tinye a:

• akụkụ, nke na-edina megide ụkwụ na-nkọ;
• na hypotenuse nke zita ukwuu karịa ihe ọ bụla nke ụkwụ;
• nchikota nke ụkwụ karịa hypotenuse;
• ụkwụ anụ nke bụ triangle, nke dabeere na ncherita-n'akuku nke 30 degrees, ọkara nke hypotenuse, na bụ hà ya ọkara.

Dị ka ọzọ onwunwe nke geometric udi nwere ike oké Pythagorean Theorem. Ọ rụrụ ụka na na a triangle na n'akuku nke 90 degrees (akụkụ anọ), nchikota nke n'ámá nke ụkwụ nhata na square nke hypotenuse.

The nchikota nke akụkụ nke ihe isosceles triangle

Tupu mgbe anyị kwuru na ihe isosceles triangle bụ a polygon na atọ vertices, nwere abụọ hà n'akụkụ. Nke a ihe onwunwe mara geometrical ọgụgụ: na akụkụ ya isi hà. Ka anyị gosi na nke a.

Were triangle KMN, nke bụ isosceles, SC - ya isi. Anyị na-achọrọ iji gosi na ∟K = ∟N. Ya mere, ka anyị were ya MA - KMN bụ bisector anyị triangle. ICA triangle na-akpa ihe ịrịba ama nke ịha nhata bụ triangle na naa. Ya bụ, site amụma nyere na cm = nm, MA bụ a nkịtị n'akụkụ, ∟1 = ∟2, n'ihi MA - a bisector. Iji ịha nhata nke abụọ triangles, otu onye nwere ike na-arụ ụka na ∟K = ∟N. N'ihi ya, Theorem e gosipụtara.

Ma anyị nwere mmasị, ihe bụ nchikota nke akụkụ nke a triangle (isosceles). N'ihi na nke a na ọ dịghị nwere ya atụmatụ, anyị ga-amalite site Theorem tụlere na mbụ. Nke ahụ bụ, anyị nwere ike ikwu na ∟K + ∟M ∟N + = 180 Celsius, ma ọ bụ 2 x ∟K ∟M + = 180 Celsius (dị ka ∟K = ∟N). Nke a agaghị ihe onwunwe, dị ka Theorem na nchikota nke akụkụ nke a triangle gosipụtara na mbụ.

Ma e wezụga ndị na-ewere Njirimara nke nkuku nke a triangle, e nwekwara ndị dị mkpa dị na nkwupụta:

• na ihe equilateral triangle elu, nke e lowered ka isi, bụ n'out oge etiti bisector nke n'akuku nke dị n'agbata hà n'akụkụ na axis nke symmetry nke ya isi;
• etiti (bisector, elu), nke na-enwe n'akụkụ nke a geometric ọnụ ọgụgụ, na-hà.

equilateral triangle

Ọ na-akpọ nri, bụ triangle, nke na-hà niile ọzọ. Kwa n'ihi ya ka hà na akụkụ. Onye ọ bụla n'ime ha bụ 60 degrees. Ka anyị gosi na nke a onwunwe.

Ka anyị iche na anyị nwere a triangle KMN. Anyị maara na km = HM = KH. Nke a pụtara na, dị ka ihe onwunwe nke akụkụ dị ke ukot na-equilateral triangle ∟K = ∟M = ∟N. Ebe ọ bụ na, dị ka nchikota nke akụkụ nke a triangle Theorem ∟K + ∟M ∟N + = 180 Celsius, mgbe ahụ, x 3 = 180 Celsius ∟K ma ọ bụ ∟K = 60 Celsius, ∟M = 60 Celsius, ∟N = 60 Celsius. N'ihi ya, nzọrọ e gosipụtara. Dị ka hụrụ si n'elu na-egosi dabeere na n'elu Theorem, nchikota nke akụkụ nke ihe equilateral triangle, dị ka nchikota nke akụkụ nke ọ bụla ọzọ triangle bụ 180 degrees. Ọzọ egosi a Theorem adịghị mkpa.

Ka nwere ndị ụfọdụ Njirimara e ji mara nke ihe equilateral triangle:

• etiti bisector elu a geometrical ọgụgụ yiri, na ha ogologo na gbakọọ ka (a x √3): 2;
• ma ọ bụrụ na a polygon circumscribing gburugburu, mgbe ahụ, na okirikiri ga-hà (a x √3): 3;
• ma ọ bụrụ na e dere na a gburugburu equilateral triangle, ya na okirikiri ga-(a x √3): 6;
• nke ebe geometric na ọnụ ọgụgụ a gbakọọ usoro: (A2 x √3): 4.

Obtuse triangle

Site definition, ihe obtuse-angled triangle, onye nke ya na nkuku bụ n'etiti 90 180 degrees. Ma nyere eziokwu na ndị ọzọ na abụọ akụkụ nke geometric udi nkọ, o nwere ike kwubiri na ha na-adịghị gafere 90 degrees. Ya mere, nchikota nke akụkụ nke a triangle Theorem na-arụ ọrụ na ịgbakọ nchikota nke akụkụ na ihe obtuse triangle. Ya mere, anyị nwere ike n'enweghị ekwu, dabeere na n'elu Theorem na nchikota nke obtuse akụkụ nke a triangle bụ 180 degrees. Ọzọ, nke a Theorem adịghị mkpa re-àmà.