Similar Triangles
Same shape, proportional sides: AA, SAS~, SSS~.
Key idea
Same shape, proportional sides: AA, SAS~, SSS~.
In depth
Similar triangles have equal angles and proportional sides. A scale factor k relates all corresponding lengths. Two equal angles (AA) is enough to show similarity.
Worked example
Triangle with sides 3, 4, 5 and another with sides 6, 8, 10 have scale factor 2. If a similar triangle has a side of 4 matching a side of 10, the factor is 2.5, so a matching side of 3 becomes 7.5.
Formula
Real-world uses
- Measuring tall trees and buildings with shadows
- Scaling a logo or a map
Common mistake
Matching sides in the wrong order. Match opposite equal angles.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Similar Triangles?
Same shape, proportional sides: AA, SAS~, SSS~. It is a topic at the intermediate level in Geometry.
What is the formula for Similar Triangles?
The key formula is a/a′ = b/b′ = c/c′.
Where is Similar Triangles used in real life?
Real-world examples: Measuring tall trees and buildings with shadows; Scaling a logo or a map.
What should I learn before Similar Triangles?
Make sure you are comfortable with Congruent Triangles, the previous topic in Geometry.
What is a common mistake with Similar Triangles?
Matching sides in the wrong order. Match opposite equal angles.
How can I practise Similar Triangles?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Similar Triangles?
Move on to Pythagorean Theorem next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Pythagorean Theorem – In a right triangle the squares on the legs sum to the square on the hypotenuse.