Question
Asked Sep 13, 2019
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  1. State and discuss that validity of the converse, inverse and contrapositive of each of the following statements in Euclidean geometry.
  1. If two lines are parallel, they do not interset.
  2. If ∠A and ∠B are both right angles, then ∠A = ∠B.
  3. Given line m and point A not on line m, there is a circle centered at A that intersects m in at least one point.
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Expert Answer

Step 1

Definitions:

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Contrapositive: The hypothesis and conclusion of a conditional statement are switched and both are made into negatives Inverse- Both statements are made into negatives Converse- Both statements are reversed

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Step 2

1. If two lines are parallel, they do not intersect.

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Contrapositive: Iftwo lines intersect, then they are not parallel Inverse If two lines are not parallel, they intersect Converse- If two lines do not intersect, they are parallel

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Step 3

2. If ∠and ∠are both right angles, then &ang...

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Contrapositive: If ZA±ZB, then ZA and ZB are not right angles Inverse If LA and ZB are not right angles, then ZA±ZB Converse-If A= ZB, then ZA and ZB are both right angles

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