Question

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Explanation:

1. For the first blank: The Pythagorean Theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse, which matches $a^2 + b^2 = n^2$ for right $\triangle DEF$.
2. For the second blank: We know $a=a$, $b=b$, and $c=n$, so all three corresponding sides of $\triangle ABC$ and $\triangle DEF$ are equal. This fits the Side-Side-Side (SSS) Congruence Postulate.
3. For the third blank: $\angle F$ is the right angle opposite hypotenuse $n$ in $\triangle DEF$. In $\triangle ABC$, the side corresponding to $n$ is $c$, which is opposite $\angle C$. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) means this angle is congruent to $\angle F$.
4. For the fourth blank: A triangle with one right angle is, by definition, a right triangle.

Answer:

1. First blank: Pythagorean Theorem
2. Second blank: SSS Congruence Postulate
3. Third blank: $\boldsymbol{C}$
4. Fourth blank: definition of a right triangle