Question

To Complete: the statement (RW)/?=(ZR)/?=(WZ)/? in the figure shown,Given:Figure is shown below.12210202811.jpg

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asked 2021-02-11

To Complete: the statement \(\displaystyle\frac{{{R}{W}}}{?}=\frac{{{Z}{R}}}{?}=\frac{{{W}{Z}}}{?}\) in the figure shown,
Given:
Figure is shown below.
image

Answers (1)

2021-02-12
Calculation:
In \(\displaystyle\triangle{R}{W}{Z}{\quad\text{and}\quad}\triangle{Z}{W}{S}\).
\(\displaystyle\angle{W}{R}{Z}\stackrel{\sim}{=}\angle{W}{Z}{S}\therefore\)(Given)
\(\displaystyle\angle{W}\stackrel{\sim}{=}\angle{W}\therefore\)(Common)
\(\displaystyle{W}{Z}\stackrel{\sim}{=}{W}{Z}\therefore\)(Common)
By AAS similarity, \(\displaystyle\triangle{R}{W}{Z}\sim\triangle{Z}{W}{S}\).
Therefore,
\(\displaystyle\frac{{{R}{W}}}{{{Z}{W}}}=\frac{{{Z}{R}}}{{{S}{Z}}}=\frac{{{W}{Z}}}{{{W}{S}}}\)
Therefore, the answer is ZW, SZ and WS.
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