You have to show that $Δ A M P ≅ Δ A M Q$ .
In the following proof, supply the missing reasons.
Steps Reasons
(i) $P M = Q M$ (i) ...
(ii) $∠ P M A = ∠ Q M A$ (ii) ...
(iii) $A M = A M$ (iii) ...
(iv) $Δ A M P ≅ Δ A M Q$ (iv) ...

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Solution

$P M = Q M$ because,the quoted lines depict that they are of same length
$∠ P M A = ∠ Q M A$ because the marking shows that they have same angle
$A M = A M$ same side has same length
$Δ A M P ≅ Δ A M Q$ by $S A S$ criteria the tiangles are similar

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You have to show that ΔAMP ≅ AMQ.

In the following proof, supply the missing reasons.

Δ A M P ≅ Δ A M Q

\begin{matrix} S t e p s & R e a s o n s i) P M = Q M & (i) i i) ∠ P M A = ∠ Q M A & (i i) i i i) A M = A M & (i i i) i v) Δ A M P ≅ Δ A M Q & (i v) \end{matrix}

Δ A M P ≅ Δ A M Q

\begin{matrix} S t e p s & R e a s o n s i) P M = Q M & (i) i i) ∠ P M A = ∠ Q M A & (i i) i i i) A M = A M & (i i i) i v) Δ A M P ≅ Δ A M Q & (i v) \end{matrix}

Δ A M P ≅ Δ A M Q

\begin{matrix} S t e p s & R e a s o n s i) P M = Q M & i) i i) ∠ P M A = ∠ Q M A & i i) i i i) A M = A M & i i i) i v) Δ A M P ≅ Δ A M Q & i v) \end{matrix}

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