NOTES 1 2 Measuring and Constructing Segments Distance

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 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 then AB + BC = AC. • B • C

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

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

EXAMPLE # 2 Continued Using the Segment Addition Postulate E is between D and F. Find DF. DF = 6 x = 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 = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 D 7 x – 9 Step 1 Solve for x. 15 = 3 x ED = DF 3 3 4 x + 6 = 7 x – 9 – 4 x 6 = 3 x – 9 +9 15 = 3 x +9 x=5 F

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