Congruence & Similarity
Congruent and similar figures, transformations, and proofs
lessons (5)
Introduction to Congruence
Learn what congruent shapes are and how to identify them using side lengths and angle measures.
Introduction to Similarity
Learn what it means for two shapes to be similar and how to identify similar figures using proportional sides and equal angles.
Congruent Triangles
Learn what makes triangles congruent and how to prove congruence using SSS, SAS, ASA, AAS, and HL.
AA Similarity
Learn how two triangles are similar when they share two pairs of congruent angles.
ASA and AAS Congruence
Learn to prove triangles congruent using the ASA and AAS theorems.
Congruent figures are identical in shape and size - they match perfectly when placed on top of each other. Similar figures have the same shape but different sizes - one is a scaled version of the other. Understanding these relationships is essential for comparing shapes, working with scale drawings, and solving geometric problems.
Congruence is established through criteria like SSS (three sides equal), SAS (two sides and included angle), and ASA (two angles and included side). Similarity requires proportional sides and equal angles. These concepts connect to real applications from map reading to architectural blueprints to photograph enlargements.
What Students Will Learn
- Identify congruent figures using transformations
- Apply congruence criteria: SSS, SAS, ASA, AAS
- Identify similar figures and calculate scale factors
- Use proportions to find missing measurements in similar figures
- Solve real-world problems involving similarity
Frequently Asked Questions
What is the difference between congruent and similar?
Congruent figures are identical - same shape AND size. Similar figures have the same shape but can be different sizes. All congruent figures are similar, but not all similar figures are congruent.
What is a scale factor?
The scale factor is the ratio of corresponding lengths in similar figures. If one triangle has sides twice as long as another similar triangle, the scale factor is 2.
How do I prove triangles are similar?
Use AA (two angles equal), SSS (all sides proportional), or SAS (two sides proportional with included angle equal). AA is often easiest since the third angle is determined by the first two.