Question

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Answer 1

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★ Given :

• $\angle$ PQR = 40°
• $\angle$ PRQ = 20°
• $\angle$ SRQ = 40°
• $\angle$ SQR = 20°

★ To Prove :

• ∆PQR $\cong$ ∆SRQ

★ Solution :

In ∆PQR & ∆SRQ ,

• $\angle$ PQR = $\angle$ SRQ ( given )
• $\angle$ PRQ = $\angle$ SQR (given)
• QR = RQ ( common )

So ,

By Angle Side Angle ,

$\rm ∆PQR \cong ∆SRQ$

_________________________

★ Know More :

There are 4 Criteria for congruence of triangle :

1. SSS - Side Side Side
2. SAS - Side Angle Side
3. ASA - Angle Side Angle
4. RHS - Right Angle Hypotenuse Side

In , SAS and ASA congruence criteria , the intermediate angle or side is taken .

Answer 2

★ Given :

\angle∠ PQR = 40°

\angle∠ PRQ = 20°

\angle∠ SRQ = 40°

\angle∠ SQR = 20°

\begin{gathered} \\ \end{gathered}

★ To Prove :

∆PQR \cong≅ ∆SRQ

\begin{gathered} \\ \end{gathered}

★ Solution :

In ∆PQR & ∆SRQ ,

\angle∠ PQR = \angle∠ SRQ ( given )

\angle∠ PRQ = \angle∠ SQR (given)

QR = RQ ( common )

So ,

By Angle Side Angle ,

\rm ∆PQR \cong ∆SRQ∆PQR≅∆SRQ

\begin{gathered} \\ \end{gathered}

_________________________

★ Know More :

There are 4 Criteria for congruence of triangle :

SSS - Side Side Side

SAS - Side Angle Side

ASA - Angle Side Angle

RHS - Right Angle Hypotenuse Side

In , SAS and ASA congruence criteria , the intermediate angle or side is taken .

Step-by-step explanation:

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