What Is AA Similarity and How Does It Apply to Shapes?
Understanding similarity is essential for excelling in school geometry, competitive exams like JEE and NTSE, and solving real-world measurement problems. It helps you recognize when two shapes have the same form but different sizes—a skill used in map-making, construction, and design. Building this concept will clarify many topics in maths and science.
Formula Used in Similarity
The standard formula is: \( \frac{\text{Side 1 of Figure A}}{\text{Corresponding Side 1 of Figure B}} = \frac{\text{Side 2 of Figure A}}{\text{Corresponding Side 2 of Figure B}} = \frac{\text{Side 3 of Figure A}}{\text{Corresponding Side 3 of Figure B}} \). This shows sides are proportional in similar figures.
Here’s a helpful table to understand similarity more clearly:
Similarity Table
| Figure | Corresponding Angles Equal? | Sides Proportional? | Are They Similar? |
|---|---|---|---|
| Triangle A & Triangle B | Yes | Yes | Yes |
| Rectangle & Square | Yes | No | No |
| Circle 1 & Circle 2 (any radius) | Yes | Yes | Yes |
This table shows how the pattern of similarity appears in geometric figures—look for equal angles and sides in the same ratio.
Worked Example – Solving a Similarity Problem
1. Two triangles have sides in proportion: the sides of Triangle PQR are 6 cm, 8 cm, and 10 cm, and the sides of Triangle XYZ are 9 cm, 12 cm, and 15 cm.2. Compare the ratios of corresponding sides:
3. Since all ratios are equal and the triangles have the same shape, they are similar by the SSS criterion.
4. If the smallest angle in Triangle PQR is 36°, then the smallest angle in Triangle XYZ is also 36° because corresponding angles of similar triangles are equal.
5. Therefore, these two triangles are similar with a scale factor of \( \frac{2}{3} \).
Practice Problems
- Check if triangles with sides 5 cm, 7 cm, 9 cm and 10 cm, 14 cm, 18 cm are similar.
- Are two circles of radius 3 cm and 7 cm similar?
- Find the scale factor between two squares with sides 4 cm and 10 cm.
- List two real-life objects that are similar figures.
Common Mistakes to Avoid
- Confusing similarity with congruence (which means same size and same shape).
- Forgetting to compare all corresponding sides and angles before concluding figures are similar.
- Assuming same shape always means same size.
Real-World Applications
The concept of similarity is useful in architecture, photography, map scaling, and model making. Engineers use it when designing scaled-down prototypes. Vedantu helps students connect similarity to practical uses in science and engineering.
We explored the idea of similarity, key properties, formulas, and solved step-by-step examples. Recognizing similar figures helps not only in geometry but also in many real-world scenarios. Practice more with Vedantu to master these concepts confidently.
Related reading: Deepen your understanding by exploring Similar Triangles.
FAQs on Understanding Similarity in Mathematics
1. What is similarity in math?
Similarity in math means two figures have the same shape, but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion. For example, two triangles are similar if all their angles are the same and their sides have equal ratios.
2. What describes a similarity?
A similarity describes a relationship where two shapes have equal corresponding angles and proportional sides. In mathematics, it most often refers to polygons or geometric figures that are the same shape but may differ in size.
3. What is an example of a similarity?
An example of similarity is two triangles where the angles are all equal, such as a triangle with sides 3 cm, 4 cm, and 5 cm, and another with sides 6 cm, 8 cm, and 10 cm. These triangles are similar because their sides are in a 1:2 ratio, and their angles match.
4. What is the meaning of AA similarity?
AA similarity stands for Angle-Angle similarity, meaning that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar by the AA criterion. Their sides will be proportional.
5. What is similarity in geometry?
In geometry, similarity means two figures have the same shape but different sizes. Their corresponding angles are equal and corresponding sides are proportional. Examples include similar triangles and similar polygons.
6. What is similarity score on Canvas?
A similarity score on Canvas (and tools like Turnitin) shows the percentage of a student's work that matches sources in its database. A high score may mean possible plagiarism, while a low score usually shows more originality. It is mainly used for checking assignments and written work.
7. What is similarity bias?
Similarity bias refers to the tendency to prefer or favor people, ideas, or things that are similar to ourselves or our existing beliefs. It is a common concept in psychology related to social bias and affects decisions and judgments.
8. What is similarity index?
A similarity index is a number that expresses how alike two things are, often as a percentage. In plagiarism detection (like Turnitin), it shows how much of a document matches existing sources.
9. What is similarity score in Turnitin?
The similarity score in Turnitin is a percentage that indicates how much of a student’s paper matches other sources in Turnitin’s database. A higher percentage means more text is similar to existing works, and further examination is needed for possible plagiarism.
10. What is similarity in psychology?
In psychology, similarity means how much two or more people, objects, or ideas are alike in terms of characteristics, interests, or behaviors. Similarity can influence relationships and social interactions.
11. What are 5 examples of similarity?
Here are five examples of similarity in different contexts:
1. Two triangles with proportional sides and equal angles.
2. Two rectangles with corresponding sides in the same ratio.
3. Detecting similarity between essays using plagiarism tools.
4. Similarity bias affecting hiring decisions.
5. Two photos with the same proportions but different sizes.
12. Similarity meaning in Hindi
Similarity का हिंदी अर्थ है समानता या सादृश्यता। गणित में इसका अर्थ होता है दो आकृतियां जिनके आकार समान हों लेकिन आकार (Size) अलग हो सकता है, उनके कोण समान होते हैं और भुजाओं का अनुपात समान होता है।
