$S$ and $T$ are points on sides $P R$ and $Q R$ of $△ P Q R$ such that $∠ P = ∠ R T S$ . Show that $△ R P Q \sim △ R T S$ .

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Solution

In $△ R P Q$ and $△ R T S$

$∠ R$ is common

$∠ R T S = ∠ P$ (Given)

$∠ P R Q = ∠ T R S = ∠ R$ (Common)

Hence, By AA criterion of similarity, $△ R P Q \sim △ R T S$ $[h e n c e p r o v e d]$

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Similar questions

S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.

Δ P Q R

∠ P = ∠ R T S

Δ R P Q \sim Δ R T S

State True or False.
S and T are point on sides PR and QR of ∆PQR such that ∠P = ∠RTS.
Then, ∆RPQ ∼ ∆RTS.

In Fig. T is a point on side QR of △PQR and S is a point such that RT = ST. Prove that PQ + PR > QS

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