1.2 Measuring Length

1. 1.2 Measuring Length Stone High School: Geometry

2. Objectives: • Define length and congruent. • Identify and use the Segment Addition Postulate.

3. Absolute Value The absolute valueof a number is said to be the distance of that number to zero. For example, |-2| = 2

4. Definition: Length of A B a b Let A and B be points on a number line, with coordinates a and b. Then the measure of , which is called the length, is |a – b| or |b – a |.

5. Example 1:

6. Congruent • Congruent figures are figures that are the same size and shape. • If you move one of them onto the other, they will match exactly. • The symbol for congruence is . is read as "Segment XY is congruent to segment YZ."

7. In geometry, tick marks are used to show which segments are known to be congruent. A B C D

8. Segment Congruence Postulate If two segments have the same length as measured by a fair ruler, then the segments are congruent. Also, if two segments are congruent, then they have the same length as measured by a fair ruler. Example: Use the Segment Congruence Postulate to complete the following: If XY = YZ, then _________. If XY = YZ, then

9. Differences between equal signs and congruence. The equal sign compares two quantities, such as the length of two segments. The congruence sign, on the other hand, compares two objects, such as two segments with the same length or two polygons with the same size and shape.

10. Segment Addition Postulate P R Q PR RQ PQ If point R is between points P and Q on a line, then PR + RQ = PQ.

11. Examples: • If point A is between points M and B on line segment MB what is the length of MB, if MA = 30 and AB = 15. • If point A is between points M and B on line segment MB what is the length of MB, if MA = 15 and MB = 100.

12. P R Q 2x 3x Find the value of x if PR = 25.

13. P R Q 2x+1 x Find the value of x if PQ = 25.