1.1 – Identify Points, Lines and Planes
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Transcript of 1.1 – Identify Points, Lines and Planes
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1.1 – Identify Points, Lines and Planes
GeometryMs.
Rinaldi
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Undefined TermsThe words below have no formal definition, and therefore are called
undefined terms. There is agreement as to their meaning though.
Terms SymbolsPoint -
Line -
Plane -
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Definitions
• Collinear Points –
• Coplanar Points –
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EXAMPLE 1 Name points, lines, and planes
b. Name three points that are collinear.Name four points that are coplanar.
a. Give two other names for PQ and for plane R.
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EXAMPLE 2 Name points, lines and planes
1. Use the diagram in Example 1. Give two other names for ST . Name a point that is not coplanar with points Q, S, and T.
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DefinitionsTerms Symbols
Segment –
Ray –
Opposite Rays –
Segments and rays are collinear if they lie on the same line. So, opposite rays are collinear. Lines, segments, and rays are coplanar if they lie in the same plane.
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EXAMPLE 3 Name segments, rays, and opposite rays
b. Name all rays with endpoint J . Which of these rays are opposite rays?
a. Give another name for GH .
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EXAMPLE 4 Name segments, rays, and opposite rays
b. Are HJ and JH the same ray ? Are HJ and HG the same ray? Explain.
a. Give another name for EF
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Definition• Intersection –
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EXAMPLE 5 Sketch intersections of lines and planes
a. Sketch a plane and a line that is in the plane.
b. Sketch a plane and a line that does not intersect the plane.
c. Sketch a plane and a line that intersects the plane at a point.
SOLUTION
a. b. c.
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EXAMPLE 6 Sketch intersections of planes
Sketch two planes that intersect in a line.
SOLUTION
Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden.
STEP 2
Draw: the line of intersection.STEP 3
Draw: a vertical plane. Shade the plane.
STEP 1
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EXAMPLE 7 Sketch intersections of planes
Sketch two different lines that intersect a plane at the same point.
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EXAMPLE 8 Sketch intersections of planes
b. Name the intersection of plane A and plane B.
c. Name the intersection of line k and plane A.
Use the diagram at the right.
a. Name the intersection of PQ and line k.
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Homework
Pages 5 – 6 # 3-11, 13, 15-20, 22, 23, 25