1. Understanding Points, 1-1 Lines, and Planes Warm Up
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

2. Warm Up 1. x ≥ 3 2. 2 ≤ x ≤ 6 3. x < 1 OR x > 0
Graph each inequality.
1. x ≥ 3
2. 2 ≤ x ≤ 6
3. x < 1 OR x > 0 -2 2 4 2 4 6 1

3. Objectives
Identify, name, and draw points, lines, segments, rays, and planes.
Apply basic facts about points, lines, and planes.
Use length and midpoint of a segment.

4. Vocabulary undefined term point line plane collinear coplanar
segment endpoint
ray opposite rays
Postulate distance
coordinate length
congruent segments angle
vertex parallel lines
perpendicular lines

5. The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

7. Points that lie on the same line are collinear
Points that lie on the same line are collinear. K, L, and M are collinear. K, L, and N are noncollinear. Points that lie on the same plane are coplanar. Otherwise they are noncoplanar. M K L N

9. DEFINITION NAME DIAGRAM
R, SRT, TRS, or 1
An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices).

11. Example 2: Drawing Segments and Rays
Draw and label each of the following.
A. a segment with endpoints M and N.
B. opposite rays with a common endpoint T.

12. Check It Out! Example 2
Draw and label a ray with endpoint M that contains N.

13. A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

15. Recall that a system of equations is a set of two or more equations containing two or more of the same variables. The coordinates of the solution of the system satisfy all equations in the system. These coordinates also locate the point where all the graphs of the equations in the system intersect.
An intersection is the set of all points that two or more figures have in common. The next two postulates describe intersections involving lines and planes.

16. Given a point on a plane, there is one and only one line perpendicular to the plane through that point.

17. Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.

18. Example 4: Representing Intersections
A. Sketch two lines intersecting in exactly one point.
B. Sketch a figure that shows a line that lies in a plane.

19. Check It Out! Example 4
Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.

20. A ruler can be used to measure the distance between two points
A ruler can be used to measure the distance between two points. A point corresponds to one and only one number on a ruler. The number is called a coordinate. The following postulate summarizes this concept.

22. Example 1: Finding the Length of a Segment
Find each length.
A. BC
B. AC
BC = |1 – 3|
AC = |–2 – 3|
= |1 – 3|
= |– 5|
= 2
= 5

23. The distance between any two points is the absolute value of the difference of the coordinates. If the coordinates of points A and B are a and b, then the distance between A and B is |a – b| or |b – a|. The distance between A and B is also called the length of AB, or AB.
AB = |a – b| or |b - a| A a B b

24. In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC.

25. Congruent segments are segments that have the same length
Congruent segments are segments that have the same length. In the diagram, PQ = RS, so you can write PQ  RS. This is read as “segment PQ is congruent to segment RS.” Tick marks are used in a figure to show congruent segments.