A Game and Some Geometry Section 1-1 A Game and Some Geometry EQUIDISTANT equally distant

Points, Lines, and Planes Section 1-2 Points, Lines, and Planes

3 Undefined terms in Geometry: 1. 2. 3. Point Line Plane

Point - represented by a dot - a location - no length - no width - no thickness - named by a capital letter

- infinite set of points that extends in two directions - no width LINE 𝐴𝐵 , 𝐵𝐴 , line l 𝐴𝐶 , 𝐶𝐴 , 𝐵𝐶 , 𝐶𝐵 • C - infinite set of points that extends in two directions - no width - no thickness - no definite length (cannot be measured) - named by two points on the line or by a lowercase letter

COLLINEAR POINTS – NONCOLLINEAR POINTS – points all in one line points A, C, D, and B are collinear points not on the same line points A, C, D, B and E are noncollinear

PLANE - infinite set of points that creates a flat surface and extends without ending - no edges - no specific length (cannot be measured) - no specific thickness - named by a capital letter or the letters around plane M or plane XYZ * Any 3 points make a plane, 4 points to be noncoplanar

COPLANAR POINTS – NONCOPLANAR POINTS – points all in one plane points A, B, and C are coplanar points not on the same plane points A, B, C, and D are noncoplanar

2 3

(4 points not all on one plane) SPACE – INTERSECTION – set of all points (4 points not all on one plane) •D •A • C • B set of points that lie in two or more figures

Line l and line m intersect at point A. The intersection of 2 lines is a ______________. The intersection of 2 planes is a _____________. l m • A Line l and line m intersect at point A. line Plane M and plane N intersect at 𝑋𝑌 .

Line l and plane M intersect at point Q. The intersection of a plane and a line not on that plane is a ___________. point l M • Q Line l and plane M intersect at point Q.

Examples: Classify each statement as true or false.   1. 𝑃𝐹 ends at P. 2. Point S is on an infinite number of lines. 3. A plane has no thickness. 4. Collinear points are coplanar. False True True True

5. Planes have edges. 6. Two planes intersect in a line segment. 7 5. Planes have edges. 6. Two planes intersect in a line segment. 7. Two intersecting lines meet in exactly one point. 8. Points have no size. 9. Line XY can be denoted as 𝑋𝑌 or 𝑌𝑋 . False False True True True

Use the diagram below to classify each statement as true or false. 10. P is in M. 11. b is in M.   12. 𝑌𝑋 contains P. False True False

13. A in on b. 14. A and P are in M. 15. N contains P. True False True

HOMEWORK: page 7 #1-20 all (CE)