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Number two is asking what information is necessary to prove who triangles are similar by by the sas similarity theorem. So i want to prove two triangles are similar by uh by the sas similarity theorem. So what does what is s.

What does sas similarity theorem mean well it means. Its side angle side right. So this guy here is different from what we had before before.

We our question was side side side this one here is side s. Here stands for angle. And then its side right so im going to have a side side side similarity theorem and what is that what does that mean in the first place.

Let me kind of write down the formal definition of this theorem here. So it says. If an angle of one triangle is congruent.

So the same to the corresponding angle of another triangle and the lengths are proportional so plus the lengths of uh thats about plus lengths of these sides are proportional triangle is similar so what does that mean so. When we look at these two triangles here um. And they they kind of drew this out already which is great.

But im going to draw it out again. So im going to draw a triangle here and maybe a smaller triangle here. And what what what it means here is that if i have this triangle abc.

So a b c. So theres angle and then d e f. Its asking us if i have an angle between a and b this or angle b.

Here. If angle b equals angle. E here.

And if these two sides. If the two sides here. A and b and d and e are proportional.

So if i can say here. A and b. If a and b.

Over. B. And c.

Over b. Over. C.

Here. Equals d. E.

Over e f. Here. Or you can say you can flip.

This. And the the up the reciprocal will be true then these two triangles are similar right so therefore if im asking us. If these angles are the same and i want the sides to be the same i need to these two pieces of information to be to be true for to prove a similarity.

So these two things are the answer here to prove similarity using writing is not that great today sorry using sas theorem. So lets look at the answer here. And it says here side angle side.

Which is good uh two triangles would be similar if theyre able to show that two sides of the triangle abc are proportional to two sides of the triangle def. So then abc would be similar to df right so. We can say that um.

If we have a b. D. E.

A. So. A.

B. Over. D.

E. Equals. B.

C. Over. E f.

Here. Um. And.

This is. What i have as well right. Then we could surely say that the angle uh the triangle abc is similar to d e f.

Here so this here is correct so this solution here is correct. And again. They use the two sides.

Here a b. And d e. And b c.

And e f. Here or technically the four sides. But the two both sides are proportional to each other and the angles.

Here are the same so this solution. Here is correct good analysis as well. .

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