1) Draw a valid conclusion if possible:
Parallel lines do not intersect
If lines do not intersect, then they have no points in common.
**can this logical argument be identified by name? If yes, name it.
2)Draw a conclusion given AB bisects segment XT at point W
3)(just show how to write equation I can solve) Angle A is greater than twice it's complement. Find BOTH angles.
4) Write a conditional statement so both it and it's converse is true.
Thank you!
-krissy
1) Given the statements:
- Parallel lines do not intersect
- If lines do not intersect, then they have no points in common.
We can draw the conclusion that:
- Parallel lines have no points in common
This logical argument can be identified as the Law of Non-Contradiction.
2) The conclusion drawn from the statement "AB bisects segment XT at point W" is that point W is the midpoint of segment XT.
3) To write an equation for solving the problem "Angle A is greater than twice its complement," we need to define some variables. Let's say the measure of angle A is x degrees. The complement of angle A would be (90 - x) degrees.
According to the problem, we can write the equation:
x > 2(90 - x)
Now, we can solve this equation:
x > 180 - 2x
3x > 180
x > 60
So, the measure of angle A is greater than 60 degrees.
To find the measure of the complement of angle A, we substitute x = 60 into the complement equation:
90 - x = 90 - 60 = 30 degrees
Therefore, the measure of angle A is greater than 60 degrees, and its complement measures 30 degrees.
4) To write a conditional statement that is true, along with its converse, we can use the statement "If it is raining, then the ground is wet."
Conditional statement: If it is raining, then the ground is wet.
Converse of the conditional statement: If the ground is wet, then it is raining.
Both the conditional statement and its converse are true, as rain will cause the ground to become wet, and the presence of a wet ground indicates rain.