In $$ riangle N O P, \angle P \cong \angle O, O P=7 $$ and $$ N O=4 $$. Find $$ P N $$

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In $$ 	riangle N O P, \angle P \cong \angle O, O P=7 $$ and $$ N O=4 $$. Find $$ P N $$

UpStudy AI · Accepted Answer

In triangle $$ \triangle N O P $$, we are given that $$ \angle P \cong \angle O $$, which indicates that the triangle is isosceles with $$ N O = 4 $$ and $$ O P = 7 $$. Since $$ \angle P $$ and $$ \angle O $$ are congruent, the sides opposite these angles must also be equal. Therefore, we can denote $$ P N $$ as $$ x $$.

Since $$ N O $$ is opposite $$ \angle P $$ and $$ O P $$ is opposite $$ \angle O $$, we have:

$$
P N = N O
$$

Thus, we can set up the equation:

$$
x = 4
$$

Now, we can conclude that:

$$
P N = 4
$$

So, the length of $$ P N $$ is $$ 4 $$.
$$ P N = 4 $$

In \( \triangle N O P, \angle P \cong \angle O, O P=7 \) and \( N O=4 \). Find \( P N \)

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