How to Find and Match Corresponding Sides Easily
Students often need to match corresponding sides while solving triangle similarity or congruence problems in exams. Accurately identifying matching sides ensures you apply the right geometry rules—including proportionality and equality—when tackling real-world designs, proofs, and board questions.
Formula Used in Corresponding Sides
The standard formula is: \( \dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{CA}{FD} \) (for triangles ABC and DEF with corresponding sides).
Here’s a helpful table to understand corresponding sides more clearly:
Corresponding Sides Table
| Triangle Side (ABC) | Corresponds to (DEF) | Proportional (Similar)? | Equal (Congruent)? |
|---|---|---|---|
| AB | DE | Yes | Yes/No |
| BC | EF | Yes | Yes/No |
| CA | FD | Yes | Yes/No |
This table shows how the pattern of corresponding sides appears when comparing two triangles—sides in the same position are matched and checked for proportionality or equality.
Definition and How to Identify Corresponding Sides
In geometry, corresponding sides are sides that occupy the same position in different shapes or polygons. If you compare two triangles such as ABC and DEF, side AB in triangle ABC is a corresponding side to side DE in triangle DEF if they connect the same ordered pair of angles. This is crucial for triangle congruence and similar triangles problems.
To identify corresponding sides between two shapes:
2. Match sides based on their positions. For triangles, AB in one matches DE in the other if angle A matches angle D and angle B matches angle E.
3. For congruent figures: Corresponding sides should be equal.
4. For similar figures: Ratios of corresponding sides should be equal (proportional).
Check related properties in triangle theorems and properties of triangles to strengthen your understanding.
Worked Example – Solving a Corresponding Sides Problem
Example: Determine if the triangles LMN and XYZ are similar given: LM = 6, MN = 8, NL = 10, XY = 9, YZ = 12, ZX = 15.
2. Find the ratios:
- \( \dfrac{LM}{XY} = \dfrac{6}{9} = \dfrac{2}{3} \)
- \( \dfrac{MN}{YZ} = \dfrac{8}{12} = \dfrac{2}{3} \)
- \( \dfrac{NL}{ZX} = \dfrac{10}{15} = \dfrac{2}{3} \)
3. Since all ratios of corresponding sides are equal, triangles LMN and XYZ are similar.
Learn more about triangle similarity at similarity of triangles.
Practice Problems
- Identify corresponding sides in triangles PQR and STU where P maps to S, Q to T, and R to U.
- Given triangles ABC and DEF with AB = 5, BC = 7, CA = 9, DE = 10, EF = 14, FD = 18, check if they are similar.
- In quadrilaterals ABCD and PQRS, which sides correspond to each other?
- If the sides of two triangles are proportional, what can you say about their corresponding angles?
Common Mistakes to Avoid
- Confusing corresponding sides with equal sides when dealing with similar triangles—remember, similar triangles need sides to be proportional, not always equal.
- Mismatching the order of vertices, leading to incorrect side pairing.
- Ignoring angle matching—which can cause you to pair the wrong corresponding sides.
Real-World Applications
The concept of corresponding sides is used in construction, engineering, art, and map-making—where scaling and matching similar shapes is essential. At Vedantu, we show students how this concept applies in computer graphics and design as well as in mathematical proofs and congruent figures found in everyday life.
We explored the idea of corresponding sides, how to identify them, use their properties, and solve related problems—all of which are vital for mastering triangle similarity and congruence. Practice more with Vedantu and try problems from triangle congruence theorem to gain confidence with this topic.
FAQs on What Are Corresponding Sides in Geometry?
1. What is meant by corresponding sides?
In geometry, corresponding sides are pairs of sides that are in the same relative position in two or more shapes, such as triangles. When two figures are similar or congruent, their corresponding sides have special relationships, such as being proportional or equal in length.
2. What is an example of a corresponding side?
For example, if triangle ABC is similar to triangle DEF, then side AB of triangle ABC corresponds to side DE of triangle DEF because both are in the same position between the first and second vertices.
3. How do you identify corresponding sides?
To identify corresponding sides, follow these steps:
- List the vertices of both shapes in order.
- Match sides by the position of the vertices (e.g., side AB in one triangle matches side DE in the other).
- Check if the sides are between corresponding angles.
4. Are corresponding angles 180 or 90?
No, corresponding angles are not always 180° or 90°. The measure of a corresponding angle depends on the shape, but in similar or congruent triangles, corresponding angles are equal in measure, regardless of the specific value.
5. What does ‘corresponding sides of similar triangles are proportional’ mean?
It means that in similar triangles, the lengths of corresponding sides have the same ratio or proportion. For example, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.
6. What is the definition of corresponding sides in geometry?
In geometry, corresponding sides are sides found in the same relative position in different shapes, especially in figures that are similar or congruent, such as triangles or polygons.
7. Are corresponding sides of congruent triangles always equal?
Yes, in congruent triangles, all corresponding sides are exactly equal in length and all corresponding angles are equal in measure.
8. Are corresponding sides always proportional in similar triangles?
Yes, in similar triangles, the lengths of corresponding sides are always proportional. This property is used to solve many geometry problems involving similar figures.
9. What is meant by corresponding sides meaning in Hindi?
Hindi में, corresponding sides को ‘समान्तर भुजाएँ’ या ‘अनुरूप भुजाएँ’ कहा जाता है, जो दो आकृतियों में एक जैसे स्थान पर स्थित होती हैं।
10. How do you prove that corresponding sides of similar triangles are proportional?
To prove this, use the similarity criteria for triangles (like AA, SAS, or SSS). When triangles are similar, the ratios of the lengths of their corresponding sides are equal: AB/DE = BC/EF = AC/DF.
11. What are ‘corresponding sides and corresponding angles’ in triangles?
In triangles, corresponding sides are sides that have the same position in each triangle, and corresponding angles share the same position and measure in both triangles when the triangles are similar or congruent.
12. Can corresponding sides be used to find unknown side lengths in triangles?
Yes, you can use the property of proportional corresponding sides in similar triangles to find unknown side lengths by setting up and solving a proportion.
