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### Course: Class 10 (Old)>Unit 6

Lesson 2: Problems involving 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.
• I think I understand this. But why is BC used twice in the cross multiplication equation?
• The title of the video sort of answers that, since you have two triangles that are similar, corresponding sides are proportional. BC is the same side that has "different role." In one triangle, it is the hypotenuse and in the other it is a leg. There are several theorems based on these triangles.
• When are we going to use this in life?
• You'll use it in school, school is a part of life.
-.-
• 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!
• How do you know that angle B is congruent to angle D?
• It is given. Both are right angles. Because they are equal, they are congruent.
• 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.
• Could this be solved with the Pythagorean theorem?
a^2 + b^2 = c^2

We know that c = 8, and with the angles shown we can determine that a° = b° = 45°. So the other 2 lengths must be equal.

4^2 + 4^2 = 8^2 or 2^2 + 2^2 = 4^2

But,
16 + 16 = 64 or 4 + 4 = 16
Are clearly wrong.

Can anyone please shed some light on what am I missing?