1. Basic Geometric Figures
Advanced Geometry
Inductive Reasoning
Lesson 1
Basic Geometric Figures

2. What is Geometry?
Geometry is a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.

3. Undefined Terms
A point is a location in space. It has no size and no shape.
A line is made up of points. It has no thickness or width and extends infinitely in two directions.
A plane is a flat surface made up of points. It has no depth and extends infinitely in all directions.

4. Naming Figures Point: a CAPITAL letter M Line:
2 points and a line symbol
a lowercase script letter
line
Plane: P X
3 noncollinear points
plane CXG C
a CAPITAL script letter
plane P G

5. a point not contained on line a
Examples:
Use the figure to name each of the following.
a point not contained on line a M
a line containing point K
a plane containing point L

6. Collinear Are points B, A, and D collinear? YES
Are points F, E, and D collinear?
Are points C and G collinear?
NO. Point D is on a different line.
YES. There is a line that contains points C and G.

7. NO. Points G, D, and B all lie in plane GDB, but point E does not.
Coplanar
Are points G, D, B, and E coplanar? Explain.
NO. Points G, D, and B all lie in plane GDB, but point E does not.

8. 4 C, G, and B C, G, B, and A OR A, B, D, and E
Examples:
Use the figure to answer each question.
How many planes appear in this figure? 4
Name 3 points that are collinear.
C, G, and B
Name 4 points that are coplanar.
C, G, B, and A OR
A, B, D, and E

9. Example: Plane P contains lines m and n that intersect in R
Draw and label a figure for each relationship.
Plane P contains lines m and n that intersect in R

10. Line Segments Drawn as: a line with no arrowheadsB A
Named by: the 2 endpoints and a segment symbol

11. Example:
Draw and label a figure for each relationship.
Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or

12. Betweenness
If a point is between two other points on a line, addition or subtraction can be used to find a missing measure.
Example: Find the measure of each segment.
Find LM.

13. Examples:
Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

14. Red slashes on the figure also indicate that segments are congruent.
Symbol:
Red slashes on the figure also indicate that segments are congruent.

15. Midpoint
Definition: the point on a segment that divides the segment into two congruent segments

16. Bisector
Definition: any figure that divides another figure into two congruent parts