Measuring segments Measurement & reasoning and proof Number operations can be used to find and compare the lengths of segments Essential understandings: Big ideas: The ruler and segment addition postulates can be used in reasoning about lengths Reason abstractly and quantitatively Mathematical practice:

Getting ready On a freshwater fishing trip, you catch the fish below. By law, you must release any fish between 15 and 19 inches long. You need to measure your fish, but the front of the ruler on the boat is worn away. Can you keep your fish? Explain how you found your answer.

Ruler postulate Every __________ on a line can be paired with a __________ number. This makes a ________- to -________ correspondence between the ____________ on the __________ and the real numbers. The real number that corresponds to a ____________ is called the _______________ of the point. The Ruler Postulate allows you to measure lengths of segments using a given unit and to find differences between points on a number line. The Distance between points is the ____________ value of the _________________ of their coordinates.

Measuring segment lengths EX: Use the figure below. Find the length of each segment. a) b) c) d)

measurement Segment Addition Postulate: If three points are _______________ and is ______________ , then Distance Formula: Congruent Segments: segments that have the ___________ length One segment is congruent to another segment, while the length of one segment is equal to the length of another segment

Examples EX 1: In the diagram of the collinear points, Find the following lengths. a) b) c) d) EX 2: are collinear points. Find if

example EX 3: Suppose . Solve for the variable. Then find the lengths of a) b)

Example EX 4: Find the lengths of the segments between the points. a) b)

EX 5: Use the diagram to find the following a) b)

1.3 p. 21 15 – 21x3, 24 – 32 evens, 33; 38 – 42 evens, 48 – 52 evens, 56 – 70 evens 23 questions