Three students have proposed these ways to describe when two lines l and m are perpendicular: Read screenshot for info. Explain why each of these definitions is correct. What are some of the advantages and disadvantages with each?

a. The definition that l and m are perpendicular if they meet at one point and one of the angles at their point of intersection is a right angle

The above definition is correct because, where two lines intersect, forming an angle of 90° with each other, then, by definition of perpendicular lines, the direction of one line is perpendicular to the other

The advantage of the above definition are;

1) It is simply stated and therefore, will be easier to understand

2) It can be easily used to test the perpendicular relationship between two objects

Disadvantages

1) It gives limited description of the other characteristics of the line

2) It does not state if the lines extend past each other after the point at which they cross

b. For the definition, l and m are perpendicular if they meet at one point and all four of the angles at their point of intersection are right angles

The above definition is correct as it meets the condition of two lines to be perpendicular to each other

Advantages

1) It clearly describes the relationship between the lines and their appearance

2) It indicates that the sun of angles at the point of intersection is 360°

Disadvantage

1) The resulting detail of the four angles may lead to ambiguity in the case where the two lines do not cross and there are only three angles formed at the point

c. For the definition, l and m are perpendicular if they meet at one point and reflection about l maps m to itself

The above definition is correct as it indicates the requirement for the continuity of the definition of the on line after crossing the other line

Advantages

1) It defines the condition of perpendicularity without the requirement for measuring the angles

2) It states the symmetrical condition of perpendicular lines about the vertical axis

Disadvantages

1) It requires further clarification in order to be related to the original definition of perpendicular lines being lines that are at right angle to each other.

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