Name the three different types of proofs

Subject : Mathematics

Question: Name the three different types of proofs you saw in this lesson. Give a description of each.

Expert Verified Solution:

The three different types of proofs commonly used in geometry are:

Two-Column Proof: This type of proof consists of two columns — one for statements and one for reasons. Each statement logically follows the previous one, and the corresponding reason explains why each statement is true based on definitions, postulates, or previously proven theorems. This format provides a clear and organized way to present a logical argument.

Paragraph Proof: In paragraph proof, the proof is written in paragraph form, using complete sentences to explain the logical sequence of the argument. Each step is described in words, and reasons are integrated into the narrative. This type of proof is less structured than a two-column proof but allows for a more fluid explanation of the reasoning process.

Flowchart Proof: A flowchart proof uses a diagram with boxes and arrows to represent the logical flow of an argument. Each box contains a statement, and the arrows connect the boxes to show the sequence of steps and their relationships. Reasons are often included in or near the boxes to explain why each step is valid. This visual format helps illustrate the logical connections between statements and is useful for understanding complex proofs.