Chapter 2 Introducing Geometry

Lesson 2.1 Definition – a statement that clarifies or explains the meaning of a word or a phrase. Point – an undefined term. The basic unit of geometry. It has no size, is infinitely small, and has only location. Named with a capital letter.

Line – an undefined term. A straight arrangement of points. There are infinitely many points in a line. A line has infinite length but no thickness and extends forever in two directions. Named with two capital letters representing points and a line over.

Plane – an undefined term. A plane has length and width but no thickness. It is a flat surface that extends forever.

Collinear points – two or more points that lie on the same line or segment. Coplanar points – two or more points that lie on the same plane.

Space – the set of all points. Line segment – two points and all the points between them that lie on the line containing the two points. The two points are called the endpoints of the line segment.

Ray – ray AB is the part of the line AB that contains point A and all the points on line AB that are the same side of point A as point B. A is the endpoint.

Angle – two rays that share a common endpoint provided the two rays do not lie on the same line. Vertex – the corner of the angle. In this picture it is S.

Lesson 2.2 Congruent – two geometric figures are congruent if and only if they are identical in shape and size.

Lesson 2.3 Conditional statement – a statement that can be expressed as an if-then statement. For example “If a polygon is a hexagon, then it has exactly six sides.” Converse – the statement formed by reversing the two parts of a conditional statement. For example “If a polygon has exactly six sides, then it is a hexagon.”

Biconditional statement – a statement in which a conditional statement and its converse are both true and are combined into one statement. “A polygon is hexagon if and only if it has exactly six sides.” Counterexample – an example that proves a statement wrong.

Right angle – an angle whose measure is 90 degrees.

Acute angle – an angle whose measure is less than 90 degrees.

Obtuse angle – an angle whose measure is greater than 90 degrees.

Midpoint of a segment – the middle of the segment such that it divides the original segment in half.

Angle bisector – a ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure.

Lesson 2.4 Parallel lines – two or more lines that lie in the same plane and that do not intersect.

Skew lines – lines that are not in the same plane and do not intersect. An example of this would be a pencil through a piece of paper.

Perpendicular lines – two lines that intersect to form a right angle.

Complementary angles – two angles whose measure have the sum of 90 degrees.

Supplementary angles – two angles whose measure have the sum of 180 degrees.

Vertical angles – two lines intersect and the angles that are across from each other.

Linear pair of angles – two angles that form a line.

Lesson 2.5 Polygon – a closed geometric figure in a plane in which line segments connect endpoint to endpoint and each segment intersect exactly two others.

Convex polygons Concave polygons

Classify polygons SidesNameSidesNameSidesNames 3Triangles7Heptagon11undecagon 4Quadrilateral8Octagon12Dodecagon 5Pentagon9Nonagon 6Hexagon10Decagon Nn-gon

Consecutive – they are right next to each other. Perimeter – the sum of the lengths of all the sides.

Diagonal of a polygon – a segment connecting any two nonconsecutive vertices.

Equilateral polygon – a polygon whose sides are equal in measure. Equiangular polygon – a polygon whose angles are equal in measure. Regular polygon – a polygon that is both equilateral and equiangular.

Lesson 2.6 Right Triangle – a triangle with exactly one right angle. Acute triangle – a triangle with three acute angles. Obtuse triangle – a triangle with exactly one obtuse angle

Scalene triangle – a triangle with three sides of different lengths. Isosceles triangle – a triangle with at least two sides the same length. Equilateral triangle – a triangle with all sides equal.

Median of a triangle – a segment connecting the midpoint of a side to the opposite vertex.

Altitude of a triangle – a perpendicular segment from a vertex to the opposite side of the line containing the opposite side.

Trapezoid – a quadrilateral with exactly one pair of parallel sides. Lesson 2.7

Kite – a quadrilateral with exactly two pairs of distinct congruent consecutive sides.

Parallelogram – a quadrilateral in which both pairs of opposite sides are parallel.

Rhombus – an equilateral parallelogram.

Rectangle – an equiangular parallelogram Square – an equiangular rhombus and equilateral rectangle.

Lesson 2.9 Locus of points – the set of all points in a plane that satisfy some given condition or property.