Dynamic Activity
Biconditional Statements
Take Note Key Concept: Biconditional Statements
A biconditional combines
| Example | Symbols | How to Read It |
|---|---|---|
| A point is a midpoint if and only if it divides a segment into two congruent segments. |
|
“p if and only if q” |
You can write a biconditional as two conditionals that are converses.
Problem 2 Identifying the Conditionals in a Biconditional
What are the two conditional statements that form this biconditional?
A ray is an angle bisector if and only if it divides an angle into two congruent angles.
Plan
How can you separate the biconditional into two parts?
Identify the part before and the part after the phrase if and only if.
Let p and q represent the following:
p: A ray is an angle bisector.
q: A ray divides an angle into two congruent angles.
✓ Got It?
-
What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1.
As you learned in Lesson 1-2, undefined terms such as point, line, and plane are the building blocks of geometry. You understand the meanings of these terms intuitively. Then you use them to define other terms such as segment.
A good definition is a statement that can help you identify or classify an object. A good definition has several important components.
- ✓ A good definition uses clearly understood terms. These terms should be commonly understood or already defined.
- ✓ A good definition is precise. Good definitions avoid words such as large, sort of, and almost.
- ✓ A good definition is reversible. That means you can write a good definition as a true biconditional.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs