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# 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

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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