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Mathematics Grade 10
Johannesburg South District
Assignment Term 22024
4.2 ACS is a triangle. 
P is a point on 
AS and 
R is a point on 
AC such that PSRQ is a parallelogram. 
PQ intersect 
AC at 
B such that 
B is the midpoint of 
AR.QC is joined. Also, 
CR=PS,C^(˙)_(1)=50^(@) and 
BP=60mm.

Mathematics Grade 1010\newlineJohannesburg South District\newlineAssignment Term 2202422024\newline44.22 ACS is a triangle. P \mathrm{P} is a point on AS \mathrm{AS} and R \mathrm{R} is a point on AC \mathrm{AC} such that PSRQ is a parallelogram. PQ \mathrm{PQ} intersect AC A C at B B such that B B is the midpoint of AR.QC A R . Q C is joined. Also, CR=PS,C˙1=50 \mathrm{CR}=\mathrm{PS}, \dot{C}_{1}=50^{\circ} and AS \mathrm{AS} 00.

Full solution

Q. Mathematics Grade 1010\newlineJohannesburg South District\newlineAssignment Term 2202422024\newline44.22 ACS is a triangle. P \mathrm{P} is a point on AS \mathrm{AS} and R \mathrm{R} is a point on AC \mathrm{AC} such that PSRQ is a parallelogram. PQ \mathrm{PQ} intersect AC A C at B B such that B B is the midpoint of AR.QC A R . Q C is joined. Also, CR=PS,C˙1=50 \mathrm{CR}=\mathrm{PS}, \dot{C}_{1}=50^{\circ} and AS \mathrm{AS} 00.
  1. Identify properties of PSRQ: Identify the properties of the parallelogram PSRQPSRQ. In a parallelogram, opposite sides are equal.
  2. Use CR=PSCR=PS to find CRCR: Since CR=PSCR=PS and PSRQPSRQ is a parallelogram, we know PS=RQPS = RQ and PQ=SRPQ = SR.
  3. Given BP=60BP=60mm and B is midpoint: Given BP=60BP = 60mm and B is the midpoint of ARAR, AB=BR=60AB = BR = 60mm.
  4. ext{PQ bisects AR at B}: Since BB is the midpoint of ARAR, and PQPQ intersects ACAC at BB, PQPQ bisects ARAR.
  5. Use BP to find CR: As CR=PSCR = PS and PS=RQPS = RQ, we can use the length of BPBP to find CRCR. Since BP=60mmBP = 60\,\text{mm}, CR=60mmCR = 60\,\text{mm}.

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