1.3 Segments, Rays, and Distance. Segment – Is the part of a line consisting of two endpoints &...
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Transcript of 1.3 Segments, Rays, and Distance. Segment – Is the part of a line consisting of two endpoints &...
![Page 1: 1.3 Segments, Rays, and Distance. Segment – Is the part of a line consisting of two endpoints & all the points between them. –Notation: 2 capital letters.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697c01f1a28abf838cd1dd4/html5/thumbnails/1.jpg)
1.3 Segments, Rays, and Distance
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• Segment – Is the part of a line consisting of two endpoints & all the points between them.– Notation: 2 capital letters with a line over
them.
– Ex:– No arrows on the end of a line. – Reads: Line segment (or segment) AB
A B
AB
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• Ray – Is the part of a line consisting of one endpoint & all the points of the line on one side of the endpoint.– Notation: 2 capital letters with a line with an
arrow on one end of it. End point always comes first.
– Ex: – Reads: Ray AB
A B
AB
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• Opposite Rays – Are two collinear rays with the same endpoint. – Opposite rays always form a line.
– Ex:
Same Line
Q R S
RQ & RS
Endpoints
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Ex.1: Naming segments and rays.
• Name 3 segments:– LP– PQ– LQ
• Name 4 rays:– LQ– QL– PL– LP– PQ
L P Q
Are LP and PL opposite rays??
No, not the same endpoints
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Group Work
• Name the following line.
• Name a segment.
• Name a ray.
X
Y
ZXY or YZ or ZX
XY or YZ or XZ
XY or YZ or ZX or YX
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Number Lines
• On a number line every point is paired with a number and every number is paired with a point.
JK M
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Number Lines
• In the diagram, point J is paired with 8
• We say 8 is the coordinate of point J.
JK M
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Length of MJ
• The length MJ, is written MJ
• It is the distance between point M and point J.
JK M
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Length of MJ
• You can find the length of a segment by subtracting the coordinates of its endpoints
JK M
• MJ = 8 – 5 = 3 • MJ = 5 - 8 = - 3
Either way as long as you take the absolute value of the answer.
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Postulates and Axioms
• Statements that are accepted without proof
• Memorize all of them– Unless it has a name– Not “Postulate 6”
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Ruler Postulate
• The points on a line can be matched, one-to-one, with the set of real numbers. The real number that corresponds to a point is the coordinate of the point.
• The distance, AB, between two points, A and B, on a line is equal to the absolute value of the difference between the coordinates of A and B.
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Remote time
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A- Sometimes B – Always C - Never
• The length of a segment is ___________ negative.
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• If point S is between points R and V, then S ____________ lies on RV.
A- Sometimes B – Always C - Never
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• A coordinate can _____________ be paired with a point on a number line.
A- Sometimes B – Always C - Never
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Segment Addition Postulate
• If B is between A and C, then AB + BC = AC. A
C
B
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Example 1
• If B is between A and C, with AB = x, BC=x+6 and AC =24. Find (a) the value of x and (b) the length of BC.
A
C
B
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Congruent
• In Geometry, two objects that have– The same size and– The same shape
are called congruent.
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Congruent __________
• Segments
• Angles
• Triangles
• Circles
• Arcs
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Congruent Segments
• Have equal lengths
• To say that DE and FG have equal lengthsDE = FG
• To say that DE and FG are congruentDE FG
2 ways to say the exact same thing
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Midpoint of a segment
• The point that divides the segment into two congruent segments.
A
B
P
3
3
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Bisector of a segment
• A line, segment, ray or plane that intersects the segment at its midpoint.
A
B
P
3
3
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Remote time
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• A bisector of a segment is ____________ a line.
A- Sometimes B – Always C - Never
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• A ray _______ has a midpoint.
A- Sometimes B – Always C - Never
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• Congruent segments ________ have equal lengths.
A- Sometimes B – Always C - Never
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• AB and BA _______ denote the same ray.
A- Sometimes B – Always C - Never