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J
LK
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J
LK
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J
LK
Points that lie on the same line are collinear.
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S
UT
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S
UT
Points that do not lie on the same line are non-collinear.
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J
LK
Point K is between points J and L.
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S
UT
Point T is not between points S and U.
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J
LK
Point K is between points J and L.For a point to be between two other
points, it must be collinear with those two points.
For any set of three points, there are two possibilities:
The points are collinear.
or
The points are non-collinear.
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J
LK
Three segments can be determined from any set of three points.
In this case the segments are:JK, KL, and JL.
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J
LK
The length of the longest segment will be equal to the sum of the lengths of the
other two segments.
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J
LK
The length of the longest segment will be equal to the sum of the lengths of the
other two segments.
JK = 5.2 cmKL = 2.8 cmJL = 8.0 cm
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27°
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Any three non-collinear points determine a triangle.
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Any three non-collinear points determine a triangle.
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Any three non-collinear points determine a triangle. The three segments determined by these three points are the sides of the
triangle.
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UT
The sum of the lengths of any two sides of a triangle is greater than the length of
the third side.
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S
UT
The sum of the lengths of any two sides of a triangle is greater than the length of
the third side. This is known is theTriangle Inequality.
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S
UT
The sum of the lengths of any two sides of a triangle is greater than the length of
the third side. This is known is theTriangle Inequality.
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S T• •UT
• •S U
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S
UT
The sum of the lengths of any two sides of a triangle is greater than the length of
the third side. This is known is theTriangle Inequality.
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• •S U
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W XY
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V
W XY
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We may assume:
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V
W XY
Z
We may assume:
straight lines,segments, and rays.
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V
W XY
Z
We may assume:
straight lines,segments, and rays.
In this diagram the segments came from lines:
VW, WY, VZ, and YZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
angles.
In this diagram these angles are depicted: V, W, Y, Z, VXW, WXZ.
VXY, and YXZ.
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V
W XY
Z
We may assume:
collinearityof points.
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V
W XY
Z
We may assume:
collinearityof points.
In this diagram:V, X, and Z are collinear.W, X, and Y are collinear.
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V
W XY
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We may assume:
betweennessof points.
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V
W XY
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We may assume:
betweennessof points.
In this diagram:Point X is between V and Z.Point X is between W and Y.
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V
W XY
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We may assume:
relative positionsof points.
In this diagram (for example):Point X is near the center.Point V is at the upper left.Point Z is at the lower right .
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V
W XY
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We may not assume:
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V
W XY
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We may not assume:
right angles
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V
W XY
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We may not assume:
right angles
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V
W XY
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We may not assume:
congruent segments
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V
W XY
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We may not assume:
congruent segments
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V
W XY
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We may not assume:
congruent angles
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V
W XY
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We may not assume:
congruent angles
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V
W XY
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We may not assume:
parallellines,
segments,or rays
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V
W XY
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We may not assume:
parallellines,
segments,or rays
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V
W XY
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We may not assume:
relative sizesof segmentsand angles
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V
W XY
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We may not assume:
relative sizesof segmentsand angles
Most diagrams are relatively accurate, butsome are not.
Points that lie on the same line are collinear.
Points that lie on the same line are collinear.Points that do not lie on the same line are
non-collinear.
Points that lie on the same line are collinear.
A set of any three points is either collinear or non-collinear.
Points that do not lie on the same line arenon-collinear.
Points that lie on the same line are collinear.
A set of any three points is either collinear or non-collinear.
Points that do not lie on the same line arenon-collinear.
For a point to be between two other points, it must be collinear with those two points.
A set of any three points determines three segments. If the points are collinear, the length of the longest segment is equal to the sum of the
lengths of the other two segments.
A set of any three points determines three segments. If the points are collinear, the length of the longest segment is equal to the sum of the
lengths of the other two segments.
If three points are non-collinear, the points determine a triangle. The sum of the lengths of any two sides of a triangle must be greater than
the length of the third side.
A set of any three points determines three segments. If the points are collinear, the length of the longest segment is equal to the sum of the
lengths of the other two segments.
If three points are non-collinear, the points determine a triangle. The sum of the lengths of any two sides of a triangle must be greater than
the length of the third side.
This is known is theTriangle Inequality.
When looking at diagrams we may
assume:
When looking at diagrams we may
assume:
Straight lines and angles
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
Right angles
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
Right anglesCongruent segments
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
Right anglesCongruent segments
Congruent angles
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
Right anglesCongruent segments
Congruent anglesParallel lines
When looking at diagrams we may
assume:
Straight lines and angles
Collinearity of points
Betweenness of points
Relative positions of points
When looking at diagrams we may not may assume:
Right anglesCongruent segments
Congruent anglesParallel lines
Relative sizes of segments and
angles
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