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Definition of Triangle

ln a Δ A B ...

Question

$ln a$ $Δ A B C, P$ and $Q$ are points on sides $A B$ and $A C$ respectively, such that PQ $∥ B C$ . If $A P = 2.4 c m, A Q = 2 c m, Q C = 3 c m$ and $B C = 10 c m,$ find $A B$ and $P Q$

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Solution

$G i v e n$ $t h a t$ $P Q | | B C$

$∠ A = ∠ A,$
$∠ P = ∠ B,$ $i n t e r i o r$ $a n g l e s$ $o n$ $s a m e$ $s i d e$ $o f$ $t r a n s v e r s a l$
$∠ Q = ∠ C,$ $i n t e r i o r$ $a n g l e s$ $o n$ $s a m e$ $s i d e$ $o f$ $t r a n s v e r s a l$
$∴$ By $A A A$ criteria, $Δ A B C \sim Δ A P Q$

$⟹ \frac{A B}{A P} = \frac{A C}{A Q} = \frac{B C}{P Q}$
$\frac{A B}{2.4} = \frac{5}{2} = \frac{10}{P Q}$
$⟹ A B = 6$ $c m, P Q = 4$ $c m$

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