# Deductive reasoning

Get the most by viewing this topic in your current grade. __Pick your course now__.

##### Intros

##### Examples

###### Lessons

**Using the Law of Detachment**

You are given the statements below. Assume these statements are true. Determine if a conclusion can be made by using the Law of Detachment.- Given the information and a statement below, determine if the conclusion is valid. Explain why it is valid or invalid.

*If two lines are perpendicular, then they intersect* **Using the Law of Syllogism**

You are given the statements below. Assume these statements are true. Determine if a conclusion can be made by using the Law of Syllogism.- If the measure of an angle is 90°, then it is a right angle.

If it is a right angle, then it is not obtuse. - If you drive a car, then you can get to the grocery store in 30 minutes

If you get to the grocery store in 30 minutes, then you will get home on time - If you drink coffee, then you will stay awake

If you stay awake, then you drink coffee.

- If the measure of an angle is 90°, then it is a right angle.
- Given the information below, determine if the conclusion is valid. Explain why it is valid or invalid.
- Given: If the shape is a square, then it is a regular polygon.

If it is a regular polygon, then all sides are equal.

Conclusion: If the shape is a square, then all sides are equal. - Given: If the shape is a square, then it is a regular polygon.

If it is a regular polygon, then all sides are equal.

Conclusion: If all sides are equal, then the shape is a square.

- Given: If the shape is a square, then it is a regular polygon.