Do SA 1 (ABCD) nen suy ra SA 1BC. Lai c6 ABCD la hinh chu nhat nen
AB 1 BC
Tir do suy ra BC 1 (SAB), suy ra BC 1 AB hay tam giac SBC vuong tai B Tuong tu, ta chung minh duoc CD ± (SAD)
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nen suy ra tam giac S C O vuong tai D Vay cac mat ben ciia hinh chop deu la nhiJng tam giac vuong.
Di^n tich xung quanh ciia hinh chop la:
S = S/iSAB + SASBC + S^sCD + SASDA
= i ( S A . A B + SB.BC + S D . C D + S A . A D )
Cty TNHH MTV DWH Khang Viet S
2 ac + bVâ +c^ + aVc^ + b^ + be 2) Ta c6: BCl(SAB) va AHc(SAB)
nen A H 1 BC . Mat khac A H 1 SB nen ta c6 A H 1 (SBC)
Suy ra A H 1 SC .
Chung minh tuong tu ta cung c6 A K 1 SC . Tir do suy ra SC 1 (AHK). 3) Ggi I la giao diem ciia SC voi mat phang (AHK), ta c6 thiet dien ciia hinh chop cat bai mat phang (AHK) la tu giac AHIK.
Ta CO hai tam giac A H I va AKI la hai tam giac vuong tai H va K. i
Do A I 1 SC nen SỊSC - SÂ ^ SI = SÂ
SC V a ^ T b ^ T c ^
Vi SC 1 (AHK) nen H I 1 SC, do do hai tam giac SIH va SBC dong dang voi nhaụ ,2 S u y r a H. S I^ j , j^ S I . B C bc^ Tuong tu: KI = «C SB — SB ^ ^ ^ ^ ^ ^ SỊCD ac â + b^+c^) 5 SD V(b2 4-c2)(a2 + b 2 + c 2 ) T r o n g t a m g i a c v u o n g SAB ta c6: A H = AB.AS SB ac AD.SA be Tuong t v : A K = = _ AD V b ^ ^
V^y di^n tich thiet dign can tinh la:
S A H I K = | ( H I . A H + K I . A K ) =
abc^
(â + b^ + c^ )V(a^ + c 2 ) ( b 2 + c 2 )
Phucmg phdp gidi Toiin Hinh hgc theo chuyen de- Nguyen PM Khdnh, Nguyen Tat Thu
Vidu 2.1.2. Cho hinh chop deu S.ABC c6 canh day bang ạ Goi M, N Ian lirgt la trung diem cua SA va SC . Tim dp dai canh ben cua hinh chop, biet: 1) A N 1 BM 2) (BMN) i . (SAC).
jCgigidị
Gpi O la tarn ciia day, ta c6 SO 1 (ABC) va AO = ^ , OE = ^ . D a t SA = h, h > 0