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Аксиомы стереометрии. Следствия из аксиом

Total questions: 15

Worksheet time: 11mins

Name
Class
Date
1.
a)

А(X1BU1)А\in\left(X_1BU_1\right)

b)

А(XMT)А\in\left(XMT\right)

c)

А(X1M1X)А\in\left(X_1M_1X\right)

d)

А(THB)А\in\left(THB\right)

2.
a)

 XАTT1=HXА\cap TT_1=H 

b)

 X1АTT1=HX_1А\cap TT_1=H 

c)

 UBTT1=HUB\cap TT_1=H 

d)

 XАTU=HXА\cap TU=H 

3.
a)

 (XMT)(TT1B)=TU\left(XMT\right)\cap\left(TT_1B\right)=TU 

b)

 (XMM1)(TMX)=XM\left(XMM_1\right)\cap\left(TMX\right)=XM 

c)

 (XMT)(TT1U)=MT\left(XMT\right)\cap\left(TT_1U\right)=MT 

d)

 (XMX1)(TT1M)=TX\left(XMX_1\right)\cap\left(TT_1M\right)=TX 

4.
a)

 (XMT)=(XUT)\left(XMT\right)=\left(XUT\right) 

b)

 (XX1T1)=(THA)\left(XX_1T_1\right)=\left(THA\right) 

c)

 (XMT)=(MTT1)\left(XMT\right)=\left(MTT_1\right) 

d)

 (AU1X1)=(MM1T1)\left(AU_1X_1\right)=\left(MM_1T_1\right) 

5.
a)

 XH(X1M1T1)=AXH\cap\left(X_1M_1T_1\right)=A 

b)

 XH(XMT)=XXH\cap\left(XMT\right)=X 

c)

 UH(U1M1T1)=UUH\cap\left(U_1M_1T_1\right)=U 

d)

 UH(T1MT)=HUH\cap\left(T_1MT\right)=H 

6.
a)

R(BCD)R\in\left(BCD\right)

b)

R(SCD)R\in\left(SCD\right)

c)

R(BCS)R\in\left(BCS\right)

d)

R(ABS)R\in\left(ABS\right)

7.
a)

 AB(APD)AB\subset\left(APD\right) 

b)

 AB(BCD)AB\subset\left(BCD\right) 

c)

 AB(BPS)AB\subset\left(BPS\right) 

d)

 AB(CQR)AB\subset\left(CQR\right) 

8.
a)

 APCQ=SAP\cap CQ=S 

b)

 RCSQ=CRC\cap SQ=C 

c)

 ABBC=BAB\cap BC=B 

d)

 DSBC=RDS\cap BC=R 

9.
a)

 C(SCD)C\in\left(SCD\right) 

b)

 C(BCS)C\in\left(BCS\right) 

c)

 C(BCD)C\in\left(BCD\right) 

d)

 C(PBS)C\in\left(PBS\right) 

10.
a)

 QR(SCD)=QQR\cap\left(SCD\right)=Q 

b)

 QR(SCD)=RQR\cap\left(SCD\right)=R 

c)

 QP(SAD)=QQP\cap\left(SAD\right)=Q 

d)

 QP(SAD)=PQP\cap\left(SAD\right)=P 

11.
a)

QK(BCD)=RQK\cap\left(BCD\right)=R

b)

KP(BDC)=MKP\cap\left(BDC\right)=M

c)

BK(SAD)=BBK\cap\left(SAD\right)=B

d)

KP(SAD)=MKP\cap\left(SAD\right)=M

12.
a)

 B(RCD)B\in\left(RCD\right) 

b)

 B(SCD)B\in\left(SCD\right) 

c)

 B(PKQ)B\in\left(PKQ\right) 

d)

 B(APM)B\in\left(APM\right) 

13.
a)

 KPAB=MKP\cap AB=M 

b)

 KPSB=KKP\cap SB=K 

c)

 KPAD=MKP\cap AD=M 

d)

 SDCB=RSD\cap CB=R 

14.
a)

 KP(ABS)KP\subset\left(ABS\right) 

b)

 MR(ADC)MR\subset\left(ADC\right) 

c)

 QR(SDC)QR\subset\left(SDC\right) 

d)

 RP(SBC)RP\subset\left(SBC\right) 

15.
a)

 (DCB)=(ABS)\left(DCB\right)=\left(ABS\right) 

b)

 (MBR)=(ADC)\left(MBR\right)=\left(ADC\right) 

c)

 (MBK)=(ABS)\left(MBK\right)=\left(ABS\right) 

d)

 (BRQ)=(QCD)\left(BRQ\right)=\left(QCD\right)