Similar triangle basics | Similarity | Geometry | Khan Academy

TL;DR

Similar triangles have the same corresponding angles and scaled-up or scaled-down corresponding sides.

Transcript

When we compare triangle ABC to triangle XYZ, it's pretty clear that they aren't congruent, that they have very different lengths of their sides. But there does seem to be something interesting about the relationship between these two triangles. One, all of their corresponding angles are the same. So the angle right here, angle BAC, is congruent to... Read More

Key Insights

• 🔺 Similar triangles have the same corresponding angles and a constant ratio between corresponding sides.
• ⚖️ The relationship between similar triangles can be described as scaling up or down.
• 🔺 Congruent triangles are identical in shape and size, while similar triangles are only identical in terms of corresponding angles and scaled corresponding sides.
• ⚖️ Similar triangles can be obtained by scaling up or down, rotating, flipping, and shifting.
• 🔺 The concept of similarity applies to all triangles, not just the specific example given.
• 🔺 Similar triangles can be determined by the ratio between corresponding sides or the equality of corresponding angles.
• 🧑‍🏭 Scaling factors determine the extent of similarity between triangles.

Questions & Answers

Q: What is the relationship between triangle ABC and triangle XYZ?

Triangle ABC and triangle XYZ are similar triangles, meaning they have the same corresponding angles and scaled-up or scaled-down corresponding sides.

Q: Can similar triangles be congruent?

No, similar triangles cannot be congruent. Congruent triangles are exactly the same, while similar triangles only have the same corresponding angles and a constant ratio between corresponding sides.

Q: How can you determine if two triangles are similar?

Two triangles are similar if all of their corresponding angles are congruent and the ratio between corresponding sides is constant.

Q: Is it possible for two triangles with different sizes to be similar?

Yes, two triangles with different sizes can be similar if their corresponding angles are congruent and the ratio between corresponding sides is the same.

Summary & Key Takeaways

• Triangle ABC and triangle XYZ are not congruent but have the same corresponding angles.

• The sides of triangle ABC are scaled-up versions of the sides of triangle XYZ.

• Similar triangles are characterized by the same corresponding angles and a constant ratio between corresponding sides.