Measuring and Constructing Segments Notes 1.2 Measuring and Constructing Segments

Distance The Distance between any 2 points is the absolute value of the difference of the coordinates. BC = |C – B| = |3 – 1| = 2 AC = |C – A| = |3 - -2| = |3 + 2| = 5

Congruent Segments Congruent Segments are segments that have the same sizw and same shape. Tick Marks are used to show congruence.

SEGMENT ADDITION POSTULATE If B is between A and C, • • • A B C then AB + BC = AC.

Using the Segment Addition Postulate EXAMPLE # 1 Using the Segment Addition Postulate M is between N and O. Find X. NM + MO = NO 17 + (3x – 5) = 5x + 2 3x + 12 = 5x + 2 – 3x – 3x 12 = 2x + 2 –2 –2 10 = 2x 2 5 = x

4 = x EXAMPLE # 2 Using the Segment Addition Postulate E is between D and F. Find DF. DE + EF = DF (3x – 1) + 13 = 6x 3x + 12 = 6x – 3x – 3x 12 = 3x 12 = 3x 3 4 = x

Using the Segment Addition Postulate EXAMPLE # 2 Continued Using the Segment Addition Postulate E is between D and F. Find DF. DF = 6x = 6(4) = 24

Midpoints The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. Example: If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3.

Example 3: Using Midpoints to Find Lengths D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D 4x + 6 7x – 9 F Step 1 Solve for x. ED = DF 3 3 15 = 3x 4x + 6 = 7x – 9 –4x –4x 6 = 3x – 9 x = 5 +9 + 9 15 = 3x

Example 3 Continued D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D 4x + 6 7x – 9 F Step 2 Find ED, DF, and EF. ED = 4x + 6 DF = 7x – 9 EF = ED + DF = 4(5) + 6 = 7(5) – 9 = 26 + 26 = 26 = 26 = 52