16. Use the LL Congruence Theorem to prove that $$ riangle H J K \cong riangle L M N $$.

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16. Use the LL Congruence Theorem to prove that $$ 	riangle H J K \cong 	riangle L M N $$.

UpStudy AI · Accepted Answer

To prove that $$ \triangle HJK \cong \triangle LMN $$ using the LL (Legs-Leg) Congruence Theorem, we need to establish that two pairs of corresponding sides (legs) of the triangles are congruent.

### Step 1: Identify the Legs
In the context of right triangles, the legs are the two sides that form the right angle. Let's denote the legs of $$ \triangle HJK $$ as follows:
- $$ HJ $$ and $$ HK $$ are the legs of $$ \triangle HJK $$.

Similarly, for $$ \triangle LMN $$:
- $$ LM $$ and $$ LN $$ are the legs of $$ \triangle LMN $$.

### Step 2: Show Congruence of the Legs
To apply the LL Congruence Theorem, we need to show that:
1. $$ HJ \cong LM $$
2. $$ HK \cong LN $$

Assuming we have the necessary information (either given or derived from a diagram), we can state:
- $$ HJ = a $$ and $$ LM = a $$ (thus $$ HJ \cong LM $$)
- $$ HK = b $$ and $$ LN = b $$ (thus $$ HK \cong LN $$)

### Step 3: Apply the LL Congruence Theorem
Since we have established that:
- $$ HJ \cong LM $$
- $$ HK \cong LN $$

By the LL Congruence Theorem, we can conclude that:
$$
\triangle HJK \cong \triangle LMN
$$

### Conclusion
Thus, we have proven that $$ \triangle HJK $$ is congruent to $$ \triangle LMN $$ using the LL Congruence Theorem.
To prove $$ \triangle HJK \cong \triangle LMN $$, show that $$ HJ \cong LM $$ and $$ HK \cong LN $$. Then, apply the LL Congruence Theorem to conclude the congruence.

Use the LL Congruence Theorem to prove that .

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