In the given figure, $R S = Q T$ and $Q S = R T .$ Prove that $P Q = P R$

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Solution

Let $Q S$ $R T$ meet at $U$

Consider $△ R U S$ and $△ Q U T$
$R S = Q T$
$Q S = R T$
$∠ R U S = ∠ Q U T$
$⟹ △ R U S, △ Q U T$ are congruent

Consider $△ P R T$ and $△ P Q S$
$∠ P R T = ∠ P Q S$
$∠ R T P = ∠ Q S P$
$R T = S Q$
$⟹ △ P R T, △ P Q S$ are congruent
$⟹ P Q = P R$

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Similar questions

In the given figure, RS = QT and QS = RT. Then which of the following options is correct?

In the given figure, $R S = Q T$ and $Q S = R T .$ Then which of the following options is correct?

\frac{Q T}{P R} = \frac{Q R}{Q S}

∠ 1 = ∠ 2

△ P Q S \sim △ T Q R

In fig, $\frac{Q T}{P R} = \frac{Q R}{Q S}$ and $∠ 1 = ∠ 2$ . Prove that $△ P Q S \sim △ T Q R$ .

Question 154 (ii)

In the given figure, $Q S ⊥ P R$ , $R T ⊥ P Q$ and QS = RT
Is $∠ P Q R = ∠ P R Q$ ? Give reason.

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