Congruent Triangles
Congruent triangles have the same shape and size.
About this topic
Congruent triangles have exactly the same shape and size, so all matching sides and angles are equal. One triangle can be moved onto the other by sliding, flipping or turning. We write △ABC ≅ △DEF with corresponding vertices in the same order.
CPCTC, "corresponding parts of congruent triangles are congruent", is used to prove that sides or angles are equal once triangles are shown congruent. Congruence is the basis for engineering with identical parts and for geometric proofs.
Worked example: triangle ABC has AB = 5, BC = 7 and angle B = 40°. Triangle DEF has DE = 5, EF = 7 and angle E = 40°. The equal angle sits between the equal sides, so SAS shows they are congruent, and we write △ABC ≅ △DEF. Then CPCTC tells us AC = DF and the other angles match. Architects use congruent parts so that identical windows, beams or tiles all fit.
The key to writing a congruence statement is order: the vertices must correspond, so A matches D, B matches E and C matches F. Mixing the order leads to false statements. Students also assume triangles that look alike in a diagram are congruent; you need given information or a theorem. Use CPCTC only after you have proved the triangles congruent, never as a reason in the middle of showing it.
Key ideas
- Corresponding sides and angles match
- Written △ABC ≅ △DEF
- Rigid motions map one onto the other
Quick check
Use cases: where Congruent Triangles helps
- Homework: review the key idea behind Congruent Triangles before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Congruent Triangles without notes.
- Visual learning: play with the interactive lab to see how Congruent Triangles changes when you adjust its inputs.
- Teaching a friend: explain Congruent Triangles in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Congruent Triangles?
Congruent triangles have the same shape and size.
What will I learn in Congruent Triangles?
Corresponding sides and angles match. Written △ABC ≅ △DEF. Rigid motions map one onto the other.
Is Congruent Triangles part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Congruent Triangles lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Congruent Triangles?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.