basic geometric figures advanced geometry inductive reasoning lesson 1
TRANSCRIPT
Basic Geometric Figures
Advanced Geometry
Inductive Reasoning
Lesson 1
What is Geometry?
Geometry is a branch of
mathematics that deals with the
measurement, properties, and
relationships of points, lines,
angles, surfaces, and solids.
Undefined TermsA 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.
Naming Figures Point: a CAPITAL letterM
Line:
• 2 points and a line symbol
• a lowercase script letter
X
R
Plane:
• 3 noncollinear points
• a CAPITAL script letter
l
CG
F
P
M
FR�������������� �
line l
plane CXG
plane P
Examples:
Use the figure to name each of the following.
a line containing point K
a plane containing point L
a point not contained on line a
M
, , ,or JK KL JL linea������������������������������������������������������������������ �����
Collinear
Are points B, A, and D collinear?
Are points F, E, and D collinear?
Are points C and G collinear?
YES
NO. Point D is on a different line.
YES. There is a line that contains points C and G.
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.
Examples:Use the figure to answer each question.
How many planes appear in this figure?
Name 3 points that are collinear.
4
C, G, and B
Name 4 points that are coplanar. C, G, B, and A
ORA, B, D, and E
Example:
Draw and label a figure for each relationship.
Plane P contains lines m and n that intersect in R
Line Segments
Drawn as: a line with no arrowheads
Named by: the 2 endpoints and a segment symbol
AB
AB
Plane R contains lines and , which intersect
at point P. Add point C on plane R so that it is not collinear with or .
AB�������������� �
DE�������������� �
AB�������������� �
DE�������������� �
Example:
Draw and label a figure for each relationship.
BetweennessIf 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.
Examples:
Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.
Congruent
Red slashes on the figure also indicate that
segments are congruent.
Symbol:
PS QR
Midpoint
Definition: the point on a segment that divides the segment into two congruent segments
Bisector
Definition: any figure that divides another figure into two congruent parts