Unit 1 Describe and Identify the three undefined terms, Understand Segment Relationships and Angle Relationships

Part 1 Definitions: Points, Lines, Planes and Segments

Undefined Terms Points, Line and Plane are all considered to be undefined terms. –This is because they can only be explained using examples and descriptions. –They can however be used to define other geometric terms and properties

Point –A location, has no shape or size –Label: Line –A line is made up of infinite points and has no thickness or width, it will continue infinitely.There is exactly one line through two points. –Label: Line Segment –Part of a line –Label: Ray –A one sided line that starts at a specific point and will continue on forever in one direction. –Label:

Collinear –Points that lie on the same line are said to be collinear –Example: Non-collinear –Points that are not on the same line are said to be non-collinear (must be three points … why?) –Example:

Plane –A flat surface made up of points, it has no depth and extends infinitely in all directions. There is exactly one plane through any three non-collinear points Coplanar –Points that lie on the same plane are said to be coplanar Non-Coplanar –Points that do not lie on the same plane are said to be non-coplanar

Intersect The intersection of two things is the place they overlap when they cross. –When two lines intersect they create a point. –When two planes intersect they create a line.

Space Space is boundless, three-dimensional set of all points. Space can contain lines and planes.

Practice Use the figure to give examples of the following: 1.Name two points. 2.Name two lines. 3.Name two segments. 4.Name two rays. 5.Name a line that does not contain point T. 6.Name a ray with point R as the endpoint. 7.Name a segment with points T and Q as its endpoints. 8.Name three collinear points. 9.Name three non-collinear points.

Congruent When two segments have the same measure they are said to be congruent Symbol: Example:

Midpoint / Segment Bisector The midpoint of a segment is the point that divides the segment into two congruent segments The Segment Bisector is a segment, line or ray that intersects another segment at its midpoint.

Example Q is the Midpoint of PR, if PQ=6x-7 and QR=5x+1, find x, PQ, QR, and PR.

Between Point B is between point A and C if and only if A, B and C are collinear and

Segment Addition Postulate – if B is between A and C, then AB + BC = AC –I–If AB + BC = AC, then B is between A and C

Example Find the length XY in the figure shown.

Example If S is between R and T and RS = 8y+4, ST = 4y+8, and RT = 15y – 9. Find y.

Part 3 Angles

Angle An angle is formed by two non-collinear rays that have a common endpoint. The rays are called sides of the angle, the common endpoint is the vertex.

Kinds of angles Right Angle Acute Angle Obtuse Angle Straight Angle / Opposite Rays

Congruent Angles Just like segments that have the same measure are congruent, so are angles that have the same measure.

Angle Addition Postulate –If R is in the interior of <PQS, then m<PQR + m<RQS = m<PQS –If m<PQR + m<RQS = m<PQS, then R is in the interior of <PQS

Example If m<BAC = 155, find m<CAT and m<BAT

Example <ABC is a straight angle, find x.

Angle Bisector A ray that divides an angle into two congruent angles is called an angle bisector.

Example Ray KM bisects <JKL, if m<JKL=72 what is the m<JKM?

Adjacent Angles are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points

Vertical Angles Two non-adjacent angles formed by two intersecting lines Vertical Angles have the same measure and are congruent

Linear Pair A pair of adjacent angles who are also supplementary

Angle Relationships Complementary Angles - Two angles whose measures have a sum of 90 Supplementary Angles - are two angles whose measures have a sum of 180

Examples

Part 3 Polygons

Polygon Closed figure whose sides are all segments. –To be a Polygon 2 things must be true Sides have common endpoints and are not collinear Sides intersect exactly two other sides

Naming a Polygon The sides of each angle in a polygon are the sides of the polygon The vertex of each angle is a vertex of the polygon They are named using all the vertices in consecutive order

The number of sides determines the name of the polygon 3 - Triangle 4 - Quadrilateral 5 - Pentagon 6 - Hexagon 7 - Heptagon 8 - Octagon 9 - Nonagon 10 - Decagon 12 - Dodecagon Anything else …. N - gon (where n represents the number of sides)

Concave VS Convex

Regular Polygon A regular polygon is a convex polygon whose sides are all congruent and whose angles are all congruent

Perimeter The perimeter of a polygon is the sum of the lengths of its sides.

Perimeter of the Coordinate Plane Find the perimeter of the triangle ABC with A(-5,1), B(-1,4), C(-6,-8)

Area Area of a polygon is the number of square units it encloses

Circle

Unit 1 The End!