Similar Triangles

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)

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.

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:

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!

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.

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

Common question:

The difference between similar triangles and congruent triangles is that the same shape and size matters to prove for congruency, but only the shape matters to prove for similarity, size does not matter in this case. Hence, we are looking for the exact same value in congruency, but the ratio of proportion in the case of similarity.

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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