Trapezoid ke eng: tlhaloso, mefuta, thepa

Khatisong ena, re tla hlahloba tlhaloso, mefuta le thepa (mabapi le diagonal, li-angles, midline, ntlha ea mateano ea mahlakoreng, joalo-joalo) ea e 'ngoe ea libopeho tse kholo tsa geometri - trapezoid.

Tlhaloso ea trapezoid

Trapezium ke quadrilateral, eo mahlakore a mabeli a eona a bapileng 'me a mang a mabeli ha a bapale.

Mahlakore a tšoanang a bitsoa metheo ea trapezoid (AD и BC), mahlakore a mang a mabeli lehlakoreng (AB le CD).

Angle botlaaseng ba trapezoid - karolo e ka hare ea trapezoid e entsoeng ke motheo le lehlakore la eona, mohlala; α и β.

Trapezoid e ngotsoe ka ho thathamisa li-vertices tsa eona, hangata ho joalo ABCD. Mme metheo e bonts'oa ka litlhaku tse nyane tsa Selatine, mohlala, a и b.

Mohala o bohareng oa trapezoid (MN) - karolo e kopanyang li-midpoints tsa mahlakore a eona a mahlakoreng.

Bophahamo ba Trapeze (h or BK) ke letlapa le huloang ho tloha motheong o mong ho ea ho o mong.

Mefuta ea trapezium

Isosceles trapezoid

Trapezoid eo mahlakore a eona a lekanang e bitsoa isosceles (kapa isosceles).

AB = CD

Rectangular trapezium

Trapezoid, eo ho eona li-angles ka bobeli ho le leng la mahlakore a eona a ka lehlakoreng le otlolohileng, e bitsoa rectangular.

∠BAD = ∠ABC = 90°

Trapezoid e fapaneng

Trapezoid ke scalene haeba mahlakore a eona a sa lekane 'me ha ho le e 'ngoe ea li-angles tse nepahetseng.

Lintho tsa Trapezoidal

Thepa e thathamisitsoeng ka tlase e sebetsa ho mofuta ofe kapa ofe oa trapezoid. Thepa le trapezoid li hlahisoa webosaeteng ea rona ka lingoliloeng tse fapaneng.

Thepa 1

Kakaretso ea li-angles tsa trapezoid tse haufi le lehlakoreng le le leng ke 180 °.

α + β = 180°

Thepa 2

Sebaka se bohareng sa trapezoid se bapile le metheo ea sona 'me se lekana le halofo ea kakaretso ea tsona.

Thepa 3

Karolo e kopanyang li-midpoints tsa li-diagonal tsa trapezoid e lutse bohareng ba eona 'me e lekana le halofo ea phapang ea metheo.

• KL karolo ya mola e kopanyang dintlha tse mahareng tsa diagonal AC и BD
• KL e lutse bohareng ba trapezium MN

Thepa 4

Lintlha tsa mateano a li-diagonal tsa trapezoid, li-extensions tsa mahlakoreng a eona le li-midpoints tsa metheo li lutse moleng o otlolohileng o tšoanang.

• DK – tswelopele ya lehlakore CD
• AK – tswelopele ya lehlakore AB
• E – bohareng ba motheo BCIe BE = EC
• F – bohareng ba motheo ADIe AF = FD

Haeba kakaretso ea li-angles botlaaseng bo le bong ke 90° (ke hore ∠DAB + ∠ADC u90d XNUMX °), ho bolelang hore likeketso tsa mahlakore a trapezoid li kopana ka lehlakoreng le letona, le karolo e hokahanyang libaka tse bohareng tsa metheo (ML) e lekana le halofo ea phapang ea bona.

Thepa 5

Li-diagonal tsa trapezoid li e arola ka li-triangles tse 4, tse peli tsa tsona (tse ka tlaase), 'me tse ling tse peli (mathokong) li lekana ka .

• ΔAED ~ ΔBEC
• S_ΔABE =S_ΔCED

Thepa 6

Karolo e fetang mateanong a li-diagonal tsa trapezoid e bapileng le metheo ea eona e ka hlahisoa ho latela bolelele ba metheo:

Thepa 7

Likarolo tse peli tsa li-angles tsa trapezoid tse nang le lehlakore le ts'oanang la lateral li pota-potile.

• AP – bisector ∠BAD
• BR – bisector ∠ABC
• AP e shebahalang hantle BR

Thepa 8

Selika-likoe se ka ngoloa feela ka trapezoid haeba kakaretso ea bolelele ba metheo ea eona e lekana le kakaretso ea bolelele ba mahlakore a eona.

Tseo. AD + BC = AB + CD

Sebaka sa selikalikoe se ngotsoeng ka trapezoid se lekana le halofo ea bophahamo ba sona: R = h/2.