Similarity example problems | Similarity | Geometry | Khan Academy

TL;DR

Two similar triangles are used to find the lengths of segments in a problem involving parallel lines and transversals.

Transcript

In this first problem over here, we're asked to find out the length of this segment, segment CE. And we have these two parallel lines. AB is parallel to DE. And then, we have these two essentially transversals that form these two triangles. So let's see what we can do here. So the first thing that might jump out at you is that this angle and this a... Read More

Key Insights

• 🔺 Two triangles with congruent corresponding angles are considered similar.
• 🙃 The ratios of corresponding sides in similar triangles are equal.
• 🪈 Writing the similarity of triangles in the correct order is crucial.
• 😵 Cross-multiplication can be used to solve for unknown side lengths in similar triangles.
• 🔺 Finding the length of a segment in a similar triangle problem involves subtracting known lengths from total lengths.
• ❓ The process of establishing similarity and finding lengths can be applied to various problem scenarios.
• 🫥 Recognizing parallel lines and transversals is important for identifying similar triangles.

Questions & Answers

Q: How are the two triangles in the problem similar?

The two triangles are similar because they have two pairs of corresponding congruent angles.

Q: Why is it important to write the similarity of the triangles in the correct order?

Writing the similarity of the triangles in the correct order ensures that the corresponding sides and angles are correctly identified, preventing errors in the calculations.

Q: What information is needed to find the length of a segment using similar triangles?

To find the length of a segment using similar triangles, you need the lengths of at least two corresponding sides or the ratios of those sides.

Q: How can you find the length of CE in the first problem?

By setting up the ratios of corresponding sides, you can cross-multiply and solve for CE, which is found to be 2.4.

Q: What is the process for finding DE in the second problem?

By establishing the similarity of the triangles and setting up the ratios of corresponding sides, you can solve for CE. Then, subtracting the known length of CD, DE is found to be 2.4 as well.

Summary & Key Takeaways

• The content explains how to find the length of a segment using similar triangles.

• Two parallel lines and transversals are used to form two similar triangles.

• The corresponding angles and sides of the triangles are used to establish similarity and find the lengths of segments.