Biconditional Statement in Geometry: Definition & Examples

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Critical Thinking and Logic in Mathematics

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:01 Conditional Statement Overview
  • 1:15 Converse Statement Overview
  • 2:00 What Are Biconditional…
  • 3:21 Examples
  • 5:12 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed Audio mode

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

In this lesson, you'll learn how to define and recognize a biconditional statement. We'll review conditional statements and their converses and look at examples of each. We'll also discuss the criteria for writing biconditional statements.

Conditional Statement Overview

When you were a child, your parents might have said, 'If you are good, then I'll give you a surprise.' This is an example of a conditional statement. Biconditional statements are partially formed from conditional statements. But before we can fully explore biconditional statements, we have to understand conditional statements and their converse statements.

Conditional statements use the words 'if' and 'then.' They have two parts: a hypothesis and a conclusion. Our example had two parts: (1) If you are good, (2) then I'll give you a surprise.

  • Our hypothesis: you are good
  • Our conclusion: I'll give you a surprise

Let's try another one: If it is sunny, then it will be a hot day.

  • Our hypothesis: it is sunny
  • Our conclusion: it will be a hot day

The thing about conditional statement is that they are not necessarily true. Our last example about the sun is not true because the sun shines in the winter, too. Therefore, as long as there is an 'if' and a hypothesis, along with a 'then' and a conclusion, you have a conditional statement.

Converse Statement Overview

Remember how we said that conditional statements have a hypothesis and a conclusion? Well, in converse statements, the hypothesis and the conclusion exchange places. When we revisit our example about the sun, the converse statement would read: If it is a hot day, then it is sunny.

  • Our hypothesis: it is a hot day
  • Our conclusion: it is sunny

Let's look at a new example in relationship to geometry:

  • Conditional statement: If a polygon is a triangle, then it has three sides.
  • Converse statement: If a polygon has three sides, then it is a triangle.

Notice that both of these statements are true. Now, let's move on to biconditional statements.

What Are Biconditional Statements?

So, now that we've reviewed conditional statements and their converses, let's take a look at biconditional statements. Biconditional statements do not use the key words 'if' and 'then.' Biconditional statements are true statements that combine the hypothesis and the conclusion with the key words 'if and only if.'

For example, the statement will take this form: (hypothesis) if and only if (conclusion). We could also write it this way: (conclusion) if and only if (hypothesis). If you figured out that both the conditional and converse statements have to be true for a biconditional statement to exist in geometry, you are correct. It's like a reversible jacket; you can wear it on both sides.

Let's rewrite our last example:

  • Conditional statement: If a polygon has three sides, then it is a triangle.
  • Converse statement: If a polygon is a triangle, then it has three sides.

Since both are statements are true, we can go ahead and make our biconditional statements:

  • A polygon is a triangle 'if and only if' it has three sides.
  • A polygon has three sides 'if and only if' it is a triangle.

Since we can write two biconditional statements, we could also define them as compound statements, since both the conditional and the converse statements have to be true. Let's practice some more.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account