Geometry Review: First Semester Definitions

Reaching a conclusion based on a pattern of specific examples is known as Inductive reasoning. A conclusion reached by using inductive reasoning is known as A conjecture. Points that lie on the same line are Collinear points. Points and lines in the same plane are Coplanar. An accepted statement of fact is a Postulate (or axiom).

A part of a line consisting of two endpoints and all the points between them is a Segment. A part of a line consisting of one endpoint and all the points on the line on one side of the endpoint is a Ray. Two collinear rays with the same endpoint are Opposite rays.

Non-parallel, non-intersecting lines are Skew lines. Two segments with the same length are Congruent segments. A figure formed by two rays with the same endpoint is called an Angle. An angle whose measure is less than 90 is an Acute angle. An angle whose measure is 90 is a Right angle.

An angle whose measure is greater than 90 is an Obtuse angle. An angle whose measure is 180 is a Straight angle. Angles with the same measure are Congruent angles. A point that divides a segment into two congruent segments is The midpoint. Two lines that intersect to form right angles are Perpendicular lines.

A line, segment, or ray that is perpendicular to a segment at its midpoint is a Perpendicular bisector. The process of making a geometric figure with a straightedge and compass is called Construction. The process of reasoning logically from given facts to a conclusion is Deductive reasoning Two angles whose sides are opposite rays are Vertical angles.

Two coplanar angles with a common side, a common vertex, and no common interior points are Adjacent angles. If the sum of the measures of two angles is 90 then the angles are Complementary. If the sum of the measures of two angles is 180 then the angles are Supplementary. A conjecture that is proven is a Theorem.

A convincing argument that uses deductive reasoning is a Proof. An angle formed by a side of a polygon and an extension of a side is an Exterior angle of the polygon. The two non-adjacent angles to an exterior angle of a triangle are Remote interior angles. A statement that follows directly from a theorem is a Corollary. A triangle with all sides congruent is an Equilateral triangle.

A triangle with at least two sides congruent is Isosceles. A triangle with no sides congruent is Scalene. A triangle with all angles congruent is Equiangular. A triangle with all acute angles is an Acute triangle. A triangle with one right angle is a Right triangle. A triangle with one obtuse angle is an Obtuse triangle.

A closed plane figure with a at least three sides is called a Polygon. A polygon where no diagonal contains points outside the polygon is called Convex. A polygon where at least one diagonal contains points outside the polygon is called Concave. A polygon with all sides congruent is Equilateral. A polygon with all angle congruent is Equiangular. A polygon that is equilateral and equiangular is Regular.

A quadrilateral with both pairs of opposite sides parallel is a Parallelogram. A parallelogram with four congruent sides is a Rhombus. A parallelogram with four right angles is a Rectangle. A parallelogram with four congruent sides and four right angles is a Square. A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent is a Kite.

A quadrilateral with exactly one pair of opposite sides parallel is a Trapezoid. A trapezoid whose nonparallel sides are congruent is an Isosceles trapezoid. A set of all points in a plane equidistant from a given point is a Circle. A segment that has one endpoint at the center of a circle and the other on the circle is a Radius. A segment that contains the center of a circle and has both endpoints on the circle is a Diameter.

A half circle is called a Semicircle. A portion of the circumference of a circle shorter than a semicircle is a Minor arc. A portion of the circumference of a circle longer than a semicircle is a Major arc. Two arcs in the same circle that have exactly one point in common are Adjacent arcs. Circles with congruent radii are Congruent circles.

Polygons with congruent corresponding parts are Congruent polygons. The ratio of the lengths of corresponding sides of two similar polygons is the Similarity ratio. A statement in if-then form is a Conditional. The part after the if in a conditional is the Hypothesis. The part following the then in a conditional is the Conclusion. The determination of whether a conditional is true or false is the Truth value.

A statement where the hypothesis and conclusion are interchanged is the Converse. A combined statement where both the original statement and its converse are true is a Biconditional. A statement where both the hypothesis and conclusion are negated is the Inverse. A statement where the hypothesis and the conclusion have been interchanged and negated is the Contrapositive.

The congruent sides of an isosceles triangle are Legs. The third side of an isosceles triangle is the Base. The angle formed by the congruent sides of an isosceles triangle is the Vertex angle. The angles opposite the congruent sides of an isosceles triangle are the Base angles. A proof consisting of a Given, a Prove, a Diagram, and Statements and Reasons is a Proof in Two-Column form.

A segment connecting the midpoints of two sides of a triangle is the Midsegment. Reasoning where all possibilities are considered and then all but one are proved false is Indirect reasoning. A set of points that meets a stated condition is called a Locus. The length of the perpendicular segment from a point to a line is the Distance from the point to the line. Three or more lines that intersect in one point are Concurrent lines.

A segment whose endpoints are a vertex and the midpoint of one side of a triangle is the Median. The perpendicular segment from a vertex to the line containing the side opposite the vertex is the Altitude. The sum of the lengths of the sides of a polygon is the Perimeter. The number of square units enclosed by the polygon is the Area. The side of a right triangle opposite the right angle is the Hypotenuse.

The other two sides of a right triangle are the Legs. Three integers that satisfy the conclusion of the Pythagorean Theorem are Pythagorean Triples. The parallel sides of a trapezoid are the Bases. The nonparallel sides are the The distance from the center of a regular polygon to a vertex is the Radius of the polygon. The perpendicular distance from the center of a regular polygon to a side is the Apothem of the polygon.

Arcs in the same circle or in congruent circles that have the same measure are Congruent arcs. The region bounded by two radii and their intercepted arc is a Sector of the circle. The part of a circle bounded by an arc and the segment joining its endpoints is a Segment of the circle.

A line in the plane of a circle that intersects the circle in exactly one point is a Tangent to circle. The point where a circle and a tangent intersect is the Point of tangency. A segment whose endpoints are on a circle is a Chord of the circle. An angle whose vertex is on a circle and whose sides are chords of the circle is an Inscribed angle. If all the vertices of a polygon lie on a circle then the polygon is Inscribed in the circle.

The End Good luck! A line that intersects a circle at two points is a Secant. An arc of a circle between the sides of an angle is called an Intercepted arc. The End Good luck!