Unit 1 Day 2

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1.3 Segments and Their Measures

• Unit 1 Day 2

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Do Now

• Evaluate each expression.
• 4 7
• 4.3 1.2
• v(4 32)
• v((-2)2 32)

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Using Segment Postulates

• In geometry, rules that are accepted without
  proof are called ___________, or axioms.
• Rules that are proved are called ___________.

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Ex. 1 Finding the Distance Between Two Points

• Measure the length of the segment to the nearest
  millimeter.

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Postulate 1 Ruler Postulate

• A line segment can lined up with coordinates on a
  number line (like a ruler).
• The distance between points A and B is the
  absolute value of the difference between the
  coordinates of A and B.
• AB is also called the length of segment AB.

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Ex. 2 Finding Distances on a Map

• Suppose the cities of Athens, Macon, and Albany,
  GA, lie in a line. If it is 80 miles from Athens
  to Macon and 90 miles from Macon to Albany, what
  is the distance from Athens to Albany?

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Postulate 2 Segment Addition Postulate

• If B is between A and C, then AB BC AC.
• If AB BC AC, then B is between A and C.
• (Recall When we say a point is between two other
  points, it implies that the three points are
  ______________.)

• Also works for more than two segments, as long as
  all points collinear

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Ex. 2A Segment Addition Postulate

• Suppose PQ 4.2 in., QR 7.5 in., and PR 11.7
  in. Is Q between P and R? How do you know?

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Distance Formula

• The distance formula is used for computing the
  distance between two points in a coordinate
  plane.
• If A is (x1, y1) and B is (x2, y2), then the
  distance between A and B is AB
  _________________.

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Ex. 3 Using the Distance Formula

• Find the length of the segments.
• AB
• AC
• AD

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Congruence

• Segments that have the same length are call
  _____________ segments.
• Lengths are equal AB ___ AD
• Segments are congruent AB __ AD

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Ex. 4 Finding Distance on a City Map

• On the map, the city blocks are each 340 feet
  apart east-west and 480 feet apart north-south.

• Find the walking (taxicab) distance between A and
  B.
• What would the (Euclidean) distance be if a
  diagonal street existed between A and B?

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Closure

• In the diagram below, could you use the segment
  addition postulate to find the distance from D to
  F? Explain why or why not.

D
3 cm.
E
F
2 cm.