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Questions and Answers
What must be done if the converse of a theorem is true?
What must be done if the converse of a theorem is true?
- It must be stated as a postulate. (correct)
- It is automatically true.
- It must be ignored.
- It must be proved as a separate theorem. (correct)
The converse of a theorem is automatically true.
The converse of a theorem is automatically true.
False (B)
State the converse of the corresponding angles postulate.
State the converse of the corresponding angles postulate.
If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
The converse of the corresponding angles postulate's hypothesis is that __________.
The converse of the corresponding angles postulate's hypothesis is that __________.
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What can be shown using the converse of the corresponding angles postulate?
What can be shown using the converse of the corresponding angles postulate?
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Study Notes
Understanding the Converse of Theorems
- The converse of a theorem involves swapping its hypothesis and conclusion.
- A converse is not inherently true; it requires validation.
- Confirmation can occur through postulation or separate proof.
Corresponding Angles Postulate
- If two coplanar lines are intersected by a transversal and corresponding angles are congruent, then those lines are parallel.
- This postulate provides a foundational criterion for establishing parallelism in geometry.
Application of the Corresponding Angles Postulate
- To confirm that two lines (line l and line m) are parallel, apply the Converse of the Corresponding Angles Postulate along with existing information about the angles formed when these lines are intersected by a transversal.
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