Geometric Proofs
A proof is a chain of logical reasons from givens to a conclusion.
About this topic
A geometric proof is a logical argument showing a statement is true, starting from given facts and using definitions, postulates and previously proven theorems, each justified by a reason. Common formats are the two-column proof, the paragraph proof and the flowchart.
Plan by marking the diagram, working backward from what you want to prove, and choosing congruence or angle theorems. Proofs build precise reasoning, a skill that carries beyond maths into law, science and computing.
Worked example: given that angle 1 and angle 2 form a linear pair and angle 2 is 110°, prove angle 1 is 70°. Statements and reasons go in two columns. Statement: angle 1 + angle 2 = 180°, reason: linear pair is supplementary. Statement: angle 1 = 180° − 110° = 70°, reason: subtraction property. Each line follows from a definition, a given fact or a theorem.
Proofs train careful reasoning that lawyers, programmers and scientists all need. Common mistakes are assuming what you must prove, relying on the diagram's appearance instead of stated facts, and giving no reason for a step. Start by marking the given information on a sketch, write what you need to show, and then work backward to see what would make it true. Finally, read the proof from top to bottom to check that each step follows from earlier ones, and that the last line is the claim.
Key ideas
- Two-column and paragraph proofs
- Use definitions, postulates and theorems
- Always state your reason for each step
Quick check
Use cases: where Geometric Proofs helps
- Homework: review the key idea behind Geometric Proofs before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Geometric Proofs without notes.
- Visual learning: play with the interactive lab to see how Geometric Proofs changes when you adjust its inputs.
- Teaching a friend: explain Geometric Proofs 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 Geometric Proofs?
A proof is a chain of logical reasons from givens to a conclusion.
What will I learn in Geometric Proofs?
Two-column and paragraph proofs. Use definitions, postulates and theorems. Always state your reason for each step.
Is Geometric Proofs 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 Geometric Proofs 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 Geometric Proofs?
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.