WEBVTT
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Given that the triangles shown are similar, determine π₯.
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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.
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In our diagram, we can see that angle πΆ and angle π are congruent.
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Angle π΄ and Angle πΏ are congruent.
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And then the remaining angles, Angle π΅ and Angle π, they are congruent.
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We know this based on the markings of the angles.
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From the markings of the angles, we can also tell which sides are proportional.
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So side π΄πΆ is proportional to side πΏπ.
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And side π΄π΅ is proportional to πΏπ.
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This means we can set up a proportion.
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So π΄πΆ is proportional to πΏπ, and π΄π΅ is proportional to πΏπ.
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So the sides on the numerators are from triangle π΄π΅πΆ, and the sides on the denominators are from triangle πΏππ.
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Now we can plug in our values.
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π΄πΆ is ten, πΏπ is π₯, π΄π΅ is nine, and πΏπ is sixteen.
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Now we will find the cross product to solve for π₯.
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So now we have nine times π₯ equals ten times sixteen.
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Letβs multiply.
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So nine π₯ equals one hundred and sixty.
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Now divide both sides by nine, and π₯ is equal to one hundred and sixty ninths.
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Therefore, πΏπ equals one hundred and sixty ninths.