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## Geometry (all content)

### Course: Geometry (all content)>Unit 12

Lesson 3: Solving similar triangles

# Solving similar triangles: same side plays different roles

Sal finds a missing side length in a problem where the same side plays different roles in two similar triangles. Created by Sal Khan.

## Want to join the conversation?

• is there a practice for similar triangles like this because i could use extra practice for this and if i could have the name for the practice that would be great thanks
• At , is principal root same as the square root of any number?
• The principal square root is the nonnegative square root -- that means the principal square root is the square root that is either 0 or positive.
• I understand all of this video.. But then I try the practice problems and I dont understand them.. How do you know where to draw another triangle to make them similar? Is there a video to learn how to do this? I never remember studying it.
• Keep reviewing, ask your parents, maybe a tutor? Try to apply it to daily things. Hope this helps.
• Is it algebraically possible for a triangle to have negative sides?
• No because distance is a scalar value and cannot be negative. This is also why we only consider the principal root in the distance formula.
• How do you know that angle B is congruent to angle D?
(1 vote)
• I don't get the cross multiplication?
(1 vote)
• Cross Multiplication is a method of proving that a proportion is valid, and exactly how it is valid. It can also be used to find a missing value in an otherwise known proportion.

An example of a proportion:

(a/b) = (x/y)

When cross multiplying a proportion such as this, you would take the top term of the first relationship (in this case, it would be a) and multiply it with the term that is down diagonally from it (in this case, y), then multiply the remaining terms (b and x).

The outcome should be similar to this:
a * y = b * x

Now, say that we knew the following:

a=1
b=2
x=2

We wished to find the value of y.

Simply solve out for y as follows.

a*y = b*x
(1) * y = (2) * (2)
1 * y = 4
divide both sides by 1, in order to eliminate the 1 from the problem.

y = 4

Hope that helped!
• is there a website also where i could practice this like very repetitively
• You could always do the 'Solving Similar Triangles 2' over and over!
• when u label the similarity between the two triangles ABC and BDC they do not share the same vertex. why is B equaled to D
• In the first triangle that he was setting up the proportions, he labeled it as ABC, if you look at how angle B in ABC has the right angle, so does angle D in triangle BDC.
• At , how can we know that triangle ABC is similar to triangle BDC if we know 2 angles in one triangle and only 1 angle on the other?
• In △ABC & △BDC
∠ABC = ∠BDC {90°}
∠BCA = ∠BCD {common ∠}
So with AA similarity criterion, △ABC ~ △BDC