# Similar Triangles

Updated: Nov 22, 2020

Dear Secondary Math students, Math Lobby will be covering the topic of Similar Triangles today**. **Similar triangles are usually tested together with Congruent Triangles in O Level Math and N Level Math examinations. Make sure to check out our earlier article on ** Congruent Triangles** if you have not done so!

__In this note, you will learn:__

**1)** __What are similar triangles?__

**2)** __Ways to prove that two triangles are similar (AA, SSS, SAS) __

**1)** __What are similar triangles?__

__What are similar triangles?__

When two triangles have the same shape and have corresponding sides and angles measured to be equal with each other, then they are said to be ** similar**. When two figures are similar, the ratios of the length of their corresponding sides are said to be equal, ie.

__2) Ways to prove that two triangles are similar (AA, SSS, SAS) __

__2) Ways to prove that two triangles are similar (AA, SSS, SAS)__

There are a few ways to prove two triangles to see whether if they are similar, which is quite identical to congruent triangles. If you haven’t check out our article on ** congruent triangles**, you can click here!

Now, let’s go through the few ways to go about this:

__1) Angle-Angle (AA)__

__1) Angle-Angle (AA)__

When **two pairs of corresponding angles are measured to be equal**

*Note: Why is Angle-Angle (AA) sufficient to prove that a triangle is similar, and not Angle-Angle-Angle (AAA)?

It is because in a triangle, there are only three interior angles, if two of them in a triangle corresponds with the other two in the other triangle, it is clear that the third angle must correspond with each other in both the triangles as well!

__2) Side-Side-Side in same proportion (SSS)__

__2) Side-Side-Side in same proportion (SSS)__

When **all three pairs of the corresponding sides are equal in proportion**, meaning that **the ratio of all three pairs of corresponding sides must be the same**

For this way of proving, an example could be: if a = 10cm, b = 6cm and c = 20cm, and if d = 5cm, then e and f must be equals to 3cm and 10cm respectively for the ratio of the corresponding sides to be the same.

__3) Side-Angle-Side (SAS)__

__3) Side-Angle-Side (SAS)__

When **two pairs of corresponding sides are equal in proportion**, and **the included angle is measured to be the same**

Common question:

__What’s the difference between congruent triangles and similar triangles?__

__What’s the difference between congruent triangles and similar triangles?__

The difference between similar triangles and congruent triangles is that the ** same shape and size** matters to prove for congruency, but

**to prove for similarity,**

__only the shape matters__**in this case. Hence, we are looking for the exact same value in congruency, but the ratio of proportion in the case of similarity.**

__size does not matter__

And that’s all we have for today, students! ** Math Lobby** hopes that after reading this article, you have a clear understanding of the definition regarding similar triangles, the numerous ways to prove the similarity of two triangles and the difference between similar triangles and congruent triangles!

As always: Work hard, stay motivated and we wish all students a successful and enjoyable journey with Math Lobby!

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