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Questions and Answers
Which are correct statements regarding proofs? (Select all that apply)
Which are correct statements regarding proofs? (Select all that apply)
- In a paragraph proof, statements and their justifications are written in sentences in a logical order. (correct)
- A flowchart proof includes a logical series of statements in boxes with connecting arrows. (correct)
- A two-column proof consists of a list of statements and the reasons the statements are true. (correct)
- A paragraph proof is a two-column proof in sentence form. (correct)
Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?
Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?
AK + BK = AC
Segment AB is congruent to segment AB. This statement shows the __________ property.
Segment AB is congruent to segment AB. This statement shows the __________ property.
reflexive
What does a two-column proof contain?
What does a two-column proof contain?
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What does a paragraph proof contain?
What does a paragraph proof contain?
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Study Notes
Proof Basics
- Proofs can be presented in various formats, including paragraph, two-column, and flowchart proofs.
- A paragraph proof is a sequence of statements and justifications written in complete sentences, logically structured.
- A two-column proof consists of statements on one side and corresponding reasons or justifications on the other.
- A flowchart proof visually represents logical steps with boxes for statements and arrows indicating connections.
Midpoints in Geometry
- If D is the midpoint of segment AB and K is the midpoint of segment BC, then it must hold that ( AK + BK = AC ).
Properties of Congruence
- The statement "Segment AB is congruent to segment AB" illustrates the reflexive property, which asserts that any segment is congruent to itself.
Characteristics of Proof Formats
- A two-column proof features a structured table layout, drawing direct links between statements and their logical reasons leading to a final conclusion.
- A paragraph proof communicates the necessary steps to reach a conclusion through clear and explanatory sentences.
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