1. Do Now: Label the plane below

2. Objectives SWBAT use the midpoint and distance formulas.

3. Definitions Midpoint: If a point is a midpoint, then it divides the segment into two congruent segments. If a point divides a segment into two congruent segments, then it is a midpoint.

4. Segment Bisector: If a segment is bisected, then it is divided at the midpoint. If a segment is divided at the midpoint, then it is bisected

5. Congruence: If two objects are congruent, then they are exactly the same size and shape. If two objects are exactly the same size and shape, then they are congruent. Congruence is marked with lines (show example of congruent lines in diagram) and we write the congruence symbol between the segments.

6. Example 1: If you know that B is the midpoint of AC and AB is 4, then what is BC? How did you solve? Statement Reason 1. B is the midpoint of AC 1. Given 2. AB = 4 2. Given 3. AB = BC 3. If B is the midpoint of AC, then it divides AC into two congruent segments. 4. BC = 4 4. If AB = BC, then BC = 4 by substitution.

7. Example 2: If AC is 6, and B is the midpoint, what’s BC? How did you figure that out? Now let’s prove it. Statement Reason

8. Example 3: If AF = 2x + 3 and FC = 4x – 1, and AC is bisected by BF, solve for x Statement Reason

9. Formulas Midpoint Formula Distance Formula

10. Steps for finding the midpoint 1)Write the formula 2)Substitute 3)Add 4)Divide

11. Example 1

12. Example 2 On a coordinate grid, a bakery is located at (2, 6). A barber shop is located at (-4, 4). Which point is exactly between the bakery and the barber shop?

13. Steps for finding the distance (look on page 18) 1.Substitute 2.Subtract 3.Square 4.Add 5.Find the square root

14. Example 3

15. Example 4

16. Guided Practice: Let’s Solve a Mystery!

17. Independent Practice See the handout!