Question

NO LINKS!! What are the true converses for each theorem? ​

Answer 1

If alternate interior angles are congruent, then lines are parallel.

If alternate exterior angles are congruent, then lines are parallel.

If corresponding angles are congruent, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

• Hypothesis: The part after the "if".
• Conclusion: The part after the "then".

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Alternate Interior

Given statement: If lines are parallel, then alternate interior angles are congruent.

• Hypothesis: "lines are parallel"
• Conclusion: "alternate interior angles are congruent"

Converse statement: If alternate interior angles are congruent, then lines are parallel.

Alternate Exterior

Given statement: If lines are parallel, then alternate exterior angles are congruent.

• Hypothesis: "lines are parallel"
• Conclusion: "alternate exterior angles are congruent"

Converse statement: If alternate exterior angles are congruent, then lines are parallel.

Corresponding

Given statement: If lines are parallel, then corresponding angles are congruent.

• Hypothesis: "lines are parallel"
• Conclusion: "corresponding angles are congruent"

Converse statement: If corresponding angles are congruent, then lines are parallel.

Consecutive Interior

Given statement: If lines are parallel, then consecutive interior angles are supplementary.

• Hypothesis: "lines are parallel"
• Conclusion: "consecutive interior angles are supplementary"

Converse statement: If consecutive interior angles are supplementary, then lines are parallel.

Consecutive Exterior

Given statement: If lines are parallel, then consecutive exterior angles are supplementary.

• Hypothesis: "lines are parallel"
• Conclusion: "consecutive exterior angles are supplementary"

Converse statement: If consecutive exterior angles are supplementary, then lines are parallel.

Answer 2

Answers:

1. If the alternate interior angles are congruent, then the lines are parallel.
2. If the alternate exterior angles are congruent, then the lines are parallel.
3. If the corresponding angles are congruent, then the lines are parallel.
4. If the consecutive interior angles are supplementary, then the lines are parallel.
5. If the consecutive exterior angles are supplementary, then the lines are parallel.

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Step-by-step explanation:

A conditional statement is of the form "if..., then..."

For example, "If it rains, then the grass gets wet" is a conditional statement.

We can have a basic template of "If P, then Q" to represent any conditional. The P and Q are placeholders for logical statements.

The converse of that conditional is "If Q, then P". We swap P and Q.

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So let's say we had this original conditional:

• "If the lines are parallel, then alternate interior angles are congruent"

The converse would be:

• "If the alternate interior angles are congruent, then the lines are parallel"

Similar ideas apply for the other converses as well.