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**Geometry** - branch of
mathematics that deals with points, lines, planes and solids and examines their
properties.

**Point**– has no size; length, width, or height. It is represented by a dot and named by a capital letter.

**Line**– set of points which has infinite length but no width or height. A line is named by a lower case letter or by any two points on the line.

**Plane**– set of points that has infinite length and width but no height. We name a plane with a capital letter.

**Space**– set of all points.

**Collinear points**– points that lie on the same line.

**Noncollinear points**– points that do not lie on the same line.

**Coplanar points**– points that lie on the same plane.

**Noncoplanar points**– points that do not lie on the same plane.

**Segment**– part of a line that consists of two points called endpoints and all points between them.

**Ray**- is the part of a line that contains an endpoint and all points extending in the other direction.

**Congruent segments**– segments that have the same length.

**Bisector of a segment**– line, ray segment, or plane that divides a segment into two congruent segments.

**Midpoint of a segment**– a point that divides the segment into two congruent segments.

**Acute angle**– angle whose measure is between 0 degrees and 90 degrees.

**Right angle**– angle whose measure is 90 degrees.

**Obtuse angle**– angle whose measure is greater than 90 degrees but less than 180 degrees.

**Straight angle**– angle whose measure is 180 degrees.

**Congruent angles**– angles that have the same measure.

**Angle bisector**– ray that divides an angle into two congruent adjacent angles.

**Triangle**– the figure formed by three segments joining three noncollinear points. Each of the three points is a vertex of the triangle and the segments are the sides.

**Acute triangle**- triangle that has all acute angles.

**Right triangle**– triangle with a right angle.

**Obtuse triangle**– triangle with an obtuse angle.

**Equiangular triangle**– triangle with all angles congruent.

**Scalene triangle**– triangle with no sides congruent.

**Isosceles triangle**– triangle with at least two sides congruent.

**Equilateral triangle**– triangle with all sides congruent.

**Adjacent angles**– two coplanar angles with a common vertex and a common side between them

**Vertical angles**– the non-adjacent angles formed by two intersecting lines.

**Complementary angles**– two angles whose sum is 90 degrees.

**Supplementary angles**– two angles whose sum is 180 degrees.

**Perpendicular lines**– two lines that intersect to form right angles.

**Parallel lines**– two lines are parallel if they are coplanar and do not intersect.

**Skew lines**– are noncoplanar lines they will not intersect.

**Polygon**– union of 3 or more coplanar segments that meet only at endpoints such that at most two segments meet at one endpoint and each segment meets exactly two other segments.

**Regular polygon**– polygon which is equilateral and equiangular.

**Congruent triangles**– two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent.

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

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

**Parallelogram**– quadrilateral with both pairs of opposite sides parallel.

**Rectangle**– parallelogram with a right angle.

**Rhombus**– parallelogram with consecutive sides congruent.

**Square**– all sides congruent and all four right angles.

**Trapezoid**– quadrilateral with exactly one pair of opposite sides parallel.

**Ratio**– comparison of two numbers by division.

**Proportion**– equation that states two ratios are equal.

**Pythagorean Theorem**– in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse

**Circle**– the set of points in a plane that are equidistant from a fixed point called the center.

**Radius**– segment whose endpoints are the center of the circle and a point on the circle.

**Chord**– segment that connects two points on the circle.

**Diameter**– chord that passes through the center of the circle.

**Secant**– line that intersects a circle in two points.

**Tangent**– line in the plane of the circle that intersects the circle in one point.

**Concentric circles**– two or more circles in the same plane with the same center.

**Congruent circles**– circles that have congruent radii.

**Sphere**– set of points in space a given distance from a given point called the center.

**Arc**– consists of two points and the continuous part of a circle between them.

**Semi-circle**– arc whose endpoints are the endpoints of a diameter.

**Minor arc**– arc whose measure is less than a semi-circle or 180 degree.

**Major arc**– arc whose measure is greater than a semi-circle or 180 degrees.

**Central angle of a circle**– angle whose vertex is the center of the circle and whose rays are radii of the circle.

**Congruent arcs**– arcs with equal measure in the same circle or in congruent circles.

**Inscribed angles**– angle whose vertex is on the circle and whose sides are chords of the circle.

**Bases**– congruent polygons lying in parallel planes.

**Altitude**– segment joining the two base planes and perpendicular to both.

**Lateral faces**– faces of a prism that are not its bases.

**Lateral edges**– intersection of adjacent lateral faces form lateral edges.

**Lateral area**– sum of the area of its lateral faces.

**Surface area**– sum of the area of all its faces.

**Volume**– number of cubic units contained in a solid.

**Right Prism**– is a prism whose lateral faces are rectangles.

**Oblique prism**– is a prism whose lateral faces are parallelograms.

**Cube**– is a prism where all sides are squares.

**Triangular prism**– is a prism whose parallel faces (the bases) are congruent triangles.

**Cylinder**– has two congruent circular bases in parallel planes.

**Cone**– has a vertex and a circular base.

**Line of symmetry**– divides a figure into two congruent halves that reflect each other.

**Perimeter**– of a polygon is the distance around the polygon.

**Area**– of any surface is the number of square units required to cover the surface.

**Volume**– of a 3-dimensional figure is the number of cubic units contained in the solid.

**Circumference**– the distance around a circle.

**Conditional statement**– a statement that can be written in an if-then form.

**Hypothesis**– in a conditional statement the statement that immediately follows the word if.

**Conclusion**– in a conditional statement the statement that immediately follows the word then.

**Converse**– the statement formed by exchanging the hypothesis and the conclusion of a conditional statement.

**Inverse**– the statement formed by negating both the hypothesis and the conclusion of a conditional statement.

**Contrapositive**– the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

**Biconditional**– the conjunction of a conditional statement and its converse.

**Deductive reasoning**– a system of reasoning that uses facts, rules,definitions, or properties to reach logical conclusions.

**Inductive reasoning**– reasoning that uses a number of specific examples to arrive at a plausible prediction.

**Proof**– a logical argument in which each statement you make is supported by a statement that is accepted as true.

**Postulate**- a statement that describes a fundamental relationship between basic terms of geometry. Postulates are accepted as true without proof.

**Theorems**– a statement or conjecture that can be proven true by given, definitions, postulates, or already proven theorems.

**Two-column proof**– a formal proof that contains statements and reasons organized in two columns.

**Paragraph proof**– an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.

**Flow proof**– a proof that organizes statements in logical order, starting with given statements. Each statement is written in a box with the reason verifying the statement written below the box.

**Conjecture**– an educated guess based on known information.

**Sine**– for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse.

**Cosine**– for an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse.

**Tangent**– for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.

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