# Reasoning and Proof

### Popular Tutorials in Reasoning and Proof

#### What is the Distributive Property?

The distributive property is a very deep math principle that helps make math work. It's the rule that lets you expand parentheses, and so it's really critical to understand if you want to get good at simplifying expressions. So check out the tutorial and let us know what you think!

#### What is a Theorem?

Theorems are a way for mathematicians to make a general mathematical statement. These statements can be used to help you solve all sorts of problems! See an introductions to theorems with this tutorial.

#### How Do You Write the Converse, Inverse, and Contrapositive of a Conditional Statement and Determine Their Truth Values?

A conditional statement is an if-then statement. For every conditional statement you can write three related statements, the converse, the inverse, and the contrapositive. The video shows how these are related.

#### How Do You Write a Biconditional Statement?

If you can write a true statement using "if and only if" , then you've got a biconditional. Learn more about biconditionals by watching the video.

#### How Do You Identify the Hypothesis and Conclusion of a Conditional Statement in If-Then Format?

People use hypotheses and conclusions all of the time, often without realizing it. Every conditional if-then statement is composed of a hypothesis and a conclusion. Check out the tutorial to learn more!

#### How Do You Use the Law of Detachment to Draw a Valid Conclusion?

See the Law of Detachment in action! This tutorial shows you an example that uses the Law of Detachment to make a conclusion.

#### How Do You Use Vertical Angles to Find Angle Measures Using Algebra?

When two lines or segments intersect, two pairs of vertical angles are formed. By the Vertical Angle Theorem, vertical angles are congruent. If you have algebraic expressions for the measures of the vertical angles, you can use the Vertical Angle Theorem to solve for their measures. Check out the tutorial to learn more!

#### What is Inductive Reasoning?

You probably observe data and patterns to make predictions or conjectures on a regular basis. If so, you are using inductive reasoning. Check out the video to learn more!

#### What is the Law of Syllogism?

If you have related conditional statements, the Law of Syllogism can help you link those conditional statements into one conditional statement. In this tutorial, you'll see how to combine related conditional statements using the Law of Syllogism.

#### What is a Biconditional Statement?

When a conditional statement and its converse are both true, you can write them as one statement called a biconditional statement. Learn more about this special kind of statement by following along with this tutorial.

#### What is a Counterexample?

It can be really tough to prove a conjecture to always be true, but it only takes one good counterexample to prove it false! Watch the tutorial to find out about counterexamples.

#### What is the Substitution Property of Equality?

If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. This property allows you to substitute quantities for each other into an expression as long as those quantities are equal. Watch this tutorial to learn about this useful property!