Advanced Geometry Inductive Reasoning Lesson 1 Basic Geometric

Advanced Geometry Inductive Reasoning Lesson 1 Basic Geometric Figures

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 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.

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

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

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

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 A B Named by: the 2 endpoints and a segment symbol

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.

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.

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

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

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