#I’ve been struggling with Similarity in Right Triangles

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paper elbow
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I can’t understand my notes anymore I need help with this question

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devout abyssBOT
gray tapir
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Just like it says in your notes, if there is an altitude to the hypotenuse in a right triangle, then all of the triangles formed are similar (~) triangles:

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⭐What are similar figures?: Similar figures are two or more shapes whose corresponding side lengths are proportional and angles are congruent.

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Therefore, we have to make a proportion for the corresponding side lengths of the shape in order to solve for AC.

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So since triangle ABD ~ ABC:

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  • AB in triangle ABD corresponds to AB in triangle ABC
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  • AD in triangle ABD corresponds to AC in triangle ABC
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Make the proportion:

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AB/AD = AC/AB

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Substitute the known values:

gray tapir
# gray tapir

this is why you learned about geometric mean in your notes

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Next, solve the proportion by cross multiplying

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I hope this helped you! If you need clarification or want some resources, let me know.

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.solved