1 2 Measuring and Constructing Segments Objectives Use

1 -2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments A ruler can be used to measure the distance between two points. A point corresponds to one and only one number on a ruler. The number is called a ______. The following postulate summarizes this concept. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments _____ – the absolute value of the difference between any two points (or coordinates. ) If the coordinates of points A and B are a and b, then the distance between A and B is |a – b| or |b – a|. _____– the distance between A and B, or AB. A a B b _____ Holt Mc. Dougal Geometry AB = |____| or |____|

1 -2 Measuring and Constructing Segments Example 2: Constructions • Turn to p. 14 in textbook to sketch, draw and construct a segment congruent to AB. • Step 1: Estimate and sketch. • Step 2: Measure and draw (with ruler. ) • Step 3: Construct and compare. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 1: Finding the Length of a Segment Find each length. A. BC Holt Mc. Dougal Geometry B. AC

1 -2 Measuring and Constructing Segments ________– segments that have the same length. In the diagram, PQ = RS, so you can write PQ RS. This is read as “segment PQ is congruent to segment RS. ” _____ are used in a figure to show congruent segments. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 2 M is between N and O. Find NO. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 3 E is between D and F. Find DF. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments _____ M of AB – the point that _____ , or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 4 a The map shows the route for a race. You are at X, 6000 ft from the first checkpoint C. The second checkpoint D is located at the midpoint between C and the end of the race Y. The total race is 15, 840 ft. How far apart are the 2 checkpoints? Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 4 b You are 1182. 5 m from the first-aid station. What is the distance to a drink station located at the midpoint between your current location and the first-aid station? Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 5 D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 Holt Mc. Dougal Geometry D 7 x – 9 F