Prove \triangle T P S ∼ \triangle T R Q.

ICSE Class X Math 2016 Solved Paper - Question 24

In the given figure $P Q R S$ is a cyclic quadrilateral $P Q$ and $S R$ produced meet at $T$ .

Question : 24 of 57

Marks: +1, -0

Prove

△ T P S ∼ △ T R Q

Solution:

∆

TPS and

∆

TRQ

\;∠ {\PST}=∠ {\RQT}

\;∠ {\SPQ}=∠ {\QRT}

[ ∵

exterior angle of cyclic quadrilateral is equal to the interior opposite angle]

∠ {\T}\;=∠ {\T}\;\;\text " (common) "\;

∴ \;\; ∆ {\TPS}\;∼ ∆ {\TRQ}\;(\;\text " By AA) "\;

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