Similarity postulates | Similarity | Geometry | Khan Academy

TL;DR

There are three postulates for determining triangle similarity: angle-angle, side-side-side, and side-angle-side.

Transcript

Let's say we have triangle ABC. It looks something like this. I want to think about the minimum amount of information. I want to come up with a couple of postulates that we can use to determine whether another triangle is similar to triangle ABC. So we already know that if all three of the corresponding angles are congruent to the corresponding ang... Read More

Key Insights

• 🔺 Three corresponding congruent angles of two triangles indicate similarity.
• 🔺 Two corresponding angles and the third angle can be determined using the angles in a triangle sum to 180 degrees.
• 🙃 If the ratio between the corresponding sides of two triangles is the same, they are similar.

Questions & Answers

Q: How can you determine if two triangles are similar based on their angles?

If all three corresponding angles of the triangles are congruent, they are similar. This is known as the angle-angle postulate.

Q: Is it possible to determine triangle similarity with just two corresponding angles?

Yes, knowing two corresponding angles is enough to determine triangle similarity. If you know two angles, you can calculate the third angle using the fact that the sum of the angles in a triangle is 180 degrees.

Q: How can the ratio between corresponding sides determine triangle similarity?

If the ratio between the corresponding sides of two triangles is the same, they are similar. This is known as the side-side-side postulate.

Q: What is the side-angle-side postulate for triangle similarity?

If two corresponding angles of two triangles are congruent and the ratio between their corresponding sides is the same, the triangles are similar. This is known as the side-angle-side postulate.

Summary & Key Takeaways

• Triangle similarity can be determined by comparing the corresponding angles of two triangles. If all three corresponding angles are congruent, the triangles are similar.

• Two corresponding angles and the ratio between their corresponding sides can also determine triangle similarity.

• The postulates for triangle similarity are angle-angle, side-side-side, and side-angle-side.