With of the following triangle congruence shortcuts could be used to prove PRQ = TRS 12210203401.jpg Given Data, /_Q ~= /_S bar(QR) ~= bar(SR) a)Side-Side-Side Postulate (SSS) b)Side-Angle-Side Postulate (SAS) c)Angle-Side-Angle Postulate (ASA) d)Angle-Angle-Side Theorem (AAS)

Question
Congruence
asked 2020-12-06
With of the following triangle congruence shortcuts could be used to prove PRQ = TRS
image
Given Data,
\(\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}\)
\(\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}\)
a)Side-Side-Side Postulate (SSS)
b)Side-Angle-Side Postulate (SAS)
c)Angle-Side-Angle Postulate (ASA)
d)Angle-Angle-Side Theorem (AAS)

Answers (1)

2020-12-07
Step 1
It is given that,
\(\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}\)
\(\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}\)
\(\displaystyle{I}{n}\triangle{P}{Q}{R}{\quad\text{and}\quad}\triangle{R}{S}{T}\),
\(\displaystyle\angle{Q}\stackrel{\sim}{=}\angle{S}\) (equal angles given)
\(\displaystyle\overline{{{Q}{R}}}\stackrel{\sim}{=}\overline{{{S}{R}}}\) ( equal sides given)
\(\displaystyle\angle{P}{R}{Q}\stackrel{\sim}{=}\angle{S}{R}{T}\) ( vertically opposite angles)
Here, two angles and one side of both triangle is equal then,
Step 2
\(\displaystyle\triangle{P}{Q}{R}\stackrel{\sim}{=}\triangle{R}{S}{T}\) (By angle-side-angle congruence)
Hence option C is correct.
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