1. Chapter 1 Foundations for Geometry
Students’ Presentation

2. 1-1 Points, Lines, and Planes
By…

3. Definition
Points: Points are the simplest figures in geometry. A point has no size, although it may represent an object with size. It is shown pictorially as a dot and is usually named using a capital letter. All geometric figures consist of points.
Line: A line is a set of points that originate from one point and extend indefinitely in two opposing directions. Often, a line is named by a lower case letter; if a line contains two points A and B, then the line can be denoted as AB or BA. Lines have no thickness, even though pictorial representations of lines do.
Plane: A plane can be modeled by a floor, a table top or a wall. Planes extend indefinitely in all directions and have no edges or thickness. Planes are often denoted by a single capital letter and represented as four-sided figures.

4. Characteristics
Point- you find them easily on lines and on coordinate planes.
Line- they are everywhere. But in geometry you find them in angles, coordinate planes, and just as themselves.
Planes- they are very obviously found, they are shapes.

5. Examples in real life

6. 1-2 Segments By

7. Definition
-A segment of a line consisting of two endpoints and all points between them
-In other words, A line that contains two end points, which may contain points in the middle

8. Characteristics
Two End points
Length can be defined(unlike a line)

9. Examples in real life

10. 1-3 Angles

11. Definition
The amount of turn between two straight lines that have a common end point which is the vertex.

12. Characteristics Acute angle less than 90 Right angle exactly 90
Obtuse angle between 90 and 180
straight angle exactly 180
Reflex angle between 180 and 360
Full angle exactly 360

13. Characteristics . Acute angle-An angle less than 90°
. Obtuse angle-An obtuse angle is one which is more than 90° but less than 180° .Right angle-
An angle which is equal to 90°, one quarter of a full revolution

14. Examples in real life:

15. 1-4 Pairs of Angles By

16. Definition -congruent angles: angles that have the same measure
-vertical lines: are the opposite angles formed by two intersecting lines
-adjacent lines: pair of angles that share a vertex and one side but do not overlap, no congruent sides
-linear lines: a straight line divided by a ray, not congruent lines
-complementary angles: two angles whose measures have a sum of 90 degrees
-supplementary angles: two angles whose measures have a sum of 180degrees

17. Characteristics Vertical angles – Are always congruent
Linear pairs – Add to 180 degrees, also adjacent
Adjacent Angles – Have common side,
don’t overlap, common vertex
Complementary Angles – Are 90 degrees
Supplementary Angles – Are 180 degrees

18. Examples in real life Supplementary Angles Adjacent Angles
Vertical Angles
Angles 1 and 2 are Linear Pair
Complementary Angles

19. 1-6 Midpoint and DistanceBy

20. Definition Mid-point -The exact middle point
“the midpoint of the line segment”
Distance- The distance between two points of a straight line that links them.

21. Definition
Midpoint of a line segment is the point that is halfway between the endpoints of the line segment
Distance is an amount of space between two things

22. Characteristics Midpoint: Distance: Middle or center
Midpoint Equation:
Distance:
Always positive
Length
Distance Equation:

23. Examples in real life

24. Examples in real life

25. 1-7 Transformations

26. Definition "Rotation" means turning around a center.
A reflection is a flip over a line.
"Translation" simply means moving, without rotating, resizing or anything else, just moving.

27. There are 41 jobs that use Transformations.
examples in real life
There are 41 jobs that use Transformations.
here are a few:
construction and building inspectors
desktop publishers
glaziers
actuaries
mathematicians
statisticians
machinists

28. Chapter 1
Class Activity

29. Find measures of all angles
Find measures of all angles. Then classify the angles as acute, right, or obtuse.