Question

day 4 - thursday, september 25th
write the converse of: if two lines are parallel, then they do not intersect.
rewrite as a biconditional: \if a polygon has 3 sides, then it is a triangle.\
day 5 - friday, september 26th
what is the slope of a line parallel to y = 2x + 5?
what is the slope of a line perpendicular to y = -1/3x + 4?

Explanation:

Step1: Find the converse

The converse of a conditional statement "If p, then q" is "If q, then p". For "If two lines are parallel, then they do not intersect", the converse is "If two lines do not intersect, then they are parallel".

Step2: Rewrite as biconditional

A biconditional statement is "p if and only if q". For "If a polygon has 3 sides, then it is a triangle", the biconditional is "A polygon is a triangle if and only if it has 3 sides".

Step3: Find slope of parallel line

For a line in the form y = mx + b (m is the slope), parallel lines have the same slope. For y = 2x+5, the slope of a parallel line is 2.

Step4: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope m is -1/m. For y=-1/3x + 4, the slope of the perpendicular line is 3.

Answer:

1. If two lines do not intersect, then they are parallel.
2. A polygon is a triangle if and only if it has 3 sides.
3. 2
4. 3