Question

1. consider this conditional statement. if two numbers are negative, then their sum is less than both numbers. lorenzo says that the inverse of the statement can be written as follows. if two numbers are positive, then their sum is greater than both numbers. is lorenzos reasoning correct? explain. use this statement for items 29 - 32. if the sum of the measures of two angles is 90°, then the angles are complementary. 29. write the inverse of the converse of the statement. 30. what is another name for the inverse of the converse? 31. write the contrapositive of the inverse of the statement. 32. what is another name for the contrapositive of the inverse? mathematical practices attend to precision 33. write a clear definition of the term adjacent angles. then use your definition to explain why ∠kjl and ∠ljm are adjacent angles but ∠kjl and ∠kjm are not adjacent angles.

Explanation:

28.

The inverse of a conditional statement "If p, then q" is "If not p, then not q". For the statement "If two numbers are negative, then their sum is less than both numbers", the inverse should be "If two numbers are not negative (i.e., at least one is non - negative), then their sum is not less than both numbers". Lorenzo's reasoning is incorrect because he changed "negative" to "positive" instead of "not negative".

The original statement is "If the sum of the measures of two angles is 90°, then the angles are complementary". The converse is "If two angles are complementary, then the sum of their measures is 90°". The inverse of the converse is "If two angles are not complementary, then the sum of their measures is not 90°".

The inverse of the converse of a conditional statement is also called the contra - inverse.

Answer:

No, Lorenzo's reasoning is incorrect. The inverse should be based on "not negative" rather than "positive".

29.