### Video Transcript

Given that the triangles shown are similar, determine π₯.

If two polygons are similar, then their corresponding angles are congruent which means theyβre the exact same measure, and the measure of their corresponding sides are proportional.

In our diagram, we can see that angle πΆ and angle π are congruent. Angle π΄ and Angle πΏ are congruent. And then the remaining angles, Angle π΅ and Angle π, they are congruent. We know this based on the markings of the angles.

From the markings of the angles, we can also tell which sides are proportional. So side π΄πΆ is proportional to side πΏπ. And side π΄π΅ is proportional to πΏπ.

This means we can set up a proportion. So π΄πΆ is proportional to πΏπ, and π΄π΅ is proportional to πΏπ. So the sides on the numerators are from triangle π΄π΅πΆ, and the sides on the denominators are from triangle πΏππ. Now we can plug in our values. π΄πΆ is ten, πΏπ is π₯, π΄π΅ is nine, and πΏπ is sixteen. Now we will find the cross product to solve for π₯.

So now we have nine times π₯ equals ten times sixteen. Letβs multiply. So nine π₯ equals one hundred and sixty. Now divide both sides by nine, and π₯ is equal to one hundred and sixty ninths.

Therefore, πΏπ equals one hundred and sixty ninths.