1-2 Vocabulary coordinate distance length construction between

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Presentation transcript:

1-2 Vocabulary coordinate distance length construction between congruent segments

FOUR BUILDING BLOCKS OF GEOMETRY Undefined Terms Point, Line Plane Definitions (Defined Terms) Definitions are always “reversible” Postulates Statements accepted as true Theorems Statements formed with deductive reasoning – can be proven

A ruler can be used to measure the distance between two points 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 coordinate. The following postulate summarizes this concept.

The distance between any two points is the absolute value of the difference of the 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 is also called the length of AB, or AB. AB = |a – b| or |b - a| A a B b

Example 1: Finding the Length of a Segment Find each length. A. BC B. AC BC = |1 – 3| AC = = |1 – 3| = = 2 =

Congruent segments are segments that have the same length Congruent segments are 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.” Tick marks are used in a figure to show congruent segments.  then = OR = then 

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.

Example 3A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH Seg. Add. Postulate 11 = 6 + GH Substitute 6 for FG and 11 for FH. – 6 –6 Subtract 6 from both sides. 5 = GH Simplify.

Example 3B: Using the Segment Addition Postulate M is between N and O. Find NO.

Lesson Quiz: 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 2. Tell whether the statements below are sometimes, always, or never true. a. If M is between K and L, then M, K, and L are collinear. b. If two segments ae congruent then they have the same length. 3. Discussion (Classroom Demonstration): Sketch, Draw and Construct a Segment 4. Know vocabulary!