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Explore critical attributes and relationships between points, lines, and planes in geometry. Learn to identify collinear, coplanar, parallel, and skew elements in geometric figures.
E N D
Named by a capital letter. A k Named by a lower case script letter, or two points on the line. k Line A B AB or BA Named by a capital script letter or by 3 non-collinear points. Q E F D Plane Q, DEF, FED, EDF, EFD Star, city on a map, bulls eye Straw, mop handle, flag pole Floor, piece of paper, soccer field
critical attributes is the classification are the critical attributes that make this definition different from other definitions.
Space Collinear Non-collinear Coplanar Non-coplanar Skew Lines Parallel Lines
point line point
Infinitely many One 6 (BC, CB, DB, BD, DC, CD)
EF, HJ, GE Three lines, AB, BC and CA Ex: Plane B, XYZ, YZX, ZXY Ex: UR, ST, TR
No, the points are not collinear because they form two distinct lines. No, the points are not coplanar because they're not on the same flat surface. There are 5 planes in the figure. ABE, AED, ADC, ABC and F Point A Point E Line ED
Yes CDHG No ABDH
Plane QRS & RST YES YES NO
Yes, they're coplanar because they can be contained in the same flat surface Yes, they're collinear because any two points create one unique line. No, they're not collinear because they can't be contained in one line. Yes, they're coplanar because any 3 non-collinear points always create a unique plane. Yes, they're coplanar because any 3 non-collinear points always create a unique plane. Yes, they're coplanar because any 3 non-collinear points always create a unique plane. The intersection of NM and LM is point M. The intersection of NM and QN is point N. The intersection of plane K and line LM is point M. The intersection of plane K and plane NMR is line NM.
Intersecting Parallel Skew Parallel No Yes No Yes