Question

Dau coroana, ma ajuta cineva la problema asta?

Answer 1

a) BAD+ADC=180 => BAD=135 (180-45)
b) 4+16/2 = 20:2 = 10cm
c) AE= diagonala in patrat
=> EAB=FAE= 45 grade (90:2)
DAB+EAB= 180 grade (135+45)
Rezulta ca D,A,E= coliniare
d) Ducem inaltimile din A si B si presupunem ca se intersecteaza cu DC in G si in P
=> GP=AB=4, trapezul este isoscel => DG=PC=6 (16-4/2)
Triunghi BPC are BCD=ADC=45 grade
BPC=90 grade => CBP=45 (190-90-45)
Rezulta ca Triunghi BPC=isoscel cu BP=PC=6 , BP=inaltime
Rezultat final: inaltime=6cm
e)AD=BC (trapez isoscel)
Aplicam Teorema lui Pitagora
BP^2 + CP^2 = BC^2
6^2 + 6^2 = BC^2
36+36=BC^2
BC= radical 72
BC=AD= 6 radical 2
f)DF si CE sunt congruente
Facem congruenta de triunghiuri intre DAF si EBC, avem AF=EB, AD=BC, FAD=EBC (360-135-90)
g)CDFE= trapez isoscel
Deoarece tocmai am facut congruenta de triunghuri (FD=EC)
Iar FE||AB, AB||CD, =>FE||CD
e)AD= 6 radical 2
Ca sa aflam AR aplicam teorema lui pitagora => AB^2+BE^2=AE^2
4^2 + 4^2 = AE^2
AE^2= 16+16
AE= radical 32
AE=4 radical 2
DE=AE+ AD
DE= 4 radical 2 + 6 radical 2
DE= 10 radical 2


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