Logical reasoning is used throughout our daily experiences but it is especially useful in the study of mathematics. When you see a set of facts, your mind automatically wants to form a conjecture or statement about the information. Look at the examples below and see if you can come up with a reasonable conjecture for each.

### Example 1

Grocery stores have certain foods on sale during the holiday seasons. Turkeys are on sale before Thanksgiving Day, foods for baking cookies and desserts are on sale around Christmas and Hanukkah, and grilling supplies and food are on sale around the Memorial Day weekend.

#### Conjecture

*People eat more of certain food during holidays and stores expect to sell more of these foods.*

### Example 2

In a set of polygons, diagonals have been drawn from one vertex and the number of triangles formed has been recorded in the table.

**Polygon** | **Number of Diagonals** | **Number of Triangles** |

Square | 1 | 2 |

Pentagon | 2 | 3 |

Hexagon | 3 | 4 |

Octagon | 5 | 6 |

#### Conjecture

*The number of triangles formed from drawing diagonals from one vertex is two less than the number of sides.*

### Example 3

A certain number, when divided by 3 and then subtracted from 57, yields the value of 35.

#### Conjecture

*The number is 66.*

The trick to using logical reasoning is to be able to support any statement (conjecture) you make with a valid reason. In geometry, we use facts, postulates, theorems, and definitions to support conjectures.

Watch the video to see what can go wrong if you don't support your conjecture.