Question

pls answer this question with euclids axiom

Answer 1

PS =SQ ( S is the midpoint of line segment PQ)
Add PS to both sides, we get
PS+PS = SQ +PS ( Axiom 2: If equals are added to equals, the wholes are equal)
So, 2PS = PQ (as PS+SQ =PQ)
PS =PQ/2 ....(1)
Next,
PR=RS (R is the midpoint of line segment PS)
Add RS to both sides, we get
PR+RS = RS +RS ( Axiom 2: If equals are added to equals, the wholes are equal)
PS = 2RS (as PR+RS = PS)
RS = PS/2 ...(2)
Put the value of PS from (1) in (2), we get
$RS \: = \frac{PQ}2÷2 \\ RS = \frac{PQ}{2} \times \frac{1}{2} \\ RS = \frac{1 }{4}PQ \:$

Answer 2

PS= SQ (S is the midpoint of the line segment PQ)
Add PS to both sides, we get PS+PS=SQ + PS (Axiom 2: If equals are added to equals, the wholes are equal)
So, 2PS = PQ (As PS+SQ=PQ)
PS= PQ/2...(1)
Next,
PR=RS (R is the midpoint of the line segment PS)
Add RS to both sides, we get PR+RS= RS+TS (Axiom 2: If equals are added to equals, the wholes are equal)
PS = 2RS (As PR+RS= PS)
RS = PS/2...(2)
Put The value of PS from (1) And (2),
We Get
RS= PQupon 2/2
RS= PQupon 2 * 1upon 2
RS= 1upon 4 PQ.