Geometry GLOSSARY |
| A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z |
A |
| Adjacent angles |
Two coplanar angles that share a vertex and a side but do not overlap
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Alternate interior angles
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Two angles that lie on opposite sides of a transversal between two lines that the transversal intersects
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Altitude of a triangle |
A perpendicular segment from a vertex of a triangle to the line that contains the opposite side
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Angle |
Two non-collinear rays having the same vertex
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Angle of depression
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When a point is viewed from a higher point, the angle that the person's line of sight makes with the horizontal
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Angle of elevation
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When a point is viewed from a lower point, the angle that the person's line of sight makes with the horizontal
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Apothem |
The distance from the center of a regular polygon to a side
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Arcs |
An unbroken part of a circle
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Area |
The amount of space in square units needed to cover a surface
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Attributes |
A quality, property, or characteristic that describes an item or a person (Ex. color, size, etc.)
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B |
Biconditional
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A statement that contains the words “if and only if” (This single statement is equivalent to writing both “if p, then q” and its converse “if q then p.)”
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Bisector |
A segment, ray or line that divides into two congruent parts
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C |
Center of a circle |
The point equal distance from all points on the circle
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Central angle
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An angle whose vertex is the center of a circle (Its measure is equal to the measure of its intercepted arc.)
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Centroid |
The centroid of the triangle is the point of congruency of the medians of the triangle.
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Chords |
A segment whose endpoints lie on the circle
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Circle |
The set of all points in a plane that are an equal distance (radius) from a given point (the center) which is also in the plane
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Circumcenter |
A circumcenter is the point of concurrency of the perpendicular bisectors of a triangle.
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Circumference |
The distance around a circle
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Circumscribed
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A circle is circumscribed about a polygon when each vertex of the polygon lies on the circle. (The polygon is I inscribed in the circle.)
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Collinear points |
Points in the same plane that lie on the same line
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Complementary angles |
Two angles whose measures add up to 90 degrees
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Concentric circles |
Concentric circles lie in the same plane and have the same center
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Conditional statements
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A statement that can be written in the form “if p, then q” (Statement p is the hypothesis and statement q is the conclusion.)
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Cone
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A three dimensional figure with one circle base and a vertex
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Congruent |
Having the same measure
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Conjecture |
Something believed to be true but not yet proven (an educated guess)
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Consecutive angles
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In a polygon, two angles that share a side
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Consecutive sides |
In a polygon, two sides that share a vertex
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Contrapositive |
The contrapositive of a conditional statement (“if p, then q” is the statement “if not q, then not p”)
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Converse
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The converse of the conditional statement interchanges the hypothesis and conclusion (“if p, then q, becomes “if q, then p”)
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Convex polygon |
A polygon in which no segment that connects two vertices can be drawn outside the polygon
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Coordinate geometry |
Geometry based on the coordinate system |
Coordinate plane |
A grid formed by two axes that intersect at the origin (The axes divided the plane into 4 equal quadrants.)
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Coplanar points |
Points that lie in the same plane
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Corollary |
A corollary of a theorem is a statement that can easily be proven by using the theorem.
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Corresponding parts
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A side (or angle) of a polygon that is matched up with a side (or angle) of a congruent or similar polygon
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Cosine |
In a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse
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Cross-section |
A cross-section is the intersection of a solid and a plane.
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Cylinder
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A space figure whose bases are circles of the same size
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D |
Deductive reasoning
| Using facts, definitions, and accepted properties in a logical order to reach a conclusion or to show that a conjecture is always true
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Dilations |
Transformations producing similar but not necessarily congruent figures
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E |
Exterior angle of a polygon
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An angle formed when one side of the polygon is extended
(The angle is adjacent to an interior angle of the polygon.)
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G |
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Geometric mean |
If a, b, and x are positive numbers, and a/x = x/b, then x is the geometric mean of a and b.
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I |
Incenter |
The incenter of a triangle is the point of congruency of the angle bisectors of the triangle.
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Inductive reasoning |
A type of reasoning in which a prediction or conclusion is based on an observed pattern |
Inscribed angle
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An angle whose vertex is on a circle and whose sides are chords of the circle
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Inscribed circle |
A circle is inscribed in a polygon if the sides of the polygon are tangent to the circle.
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Inscribed polygon |
A polygon is inscribed in a circle if the vertices of the polygon are on the circle.
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Interior angles of a polygon |
The inside angle of a polygon formed by two adjacent sides |
Inverse statement |
The inverse of the conditional statement (“if p, then q” is the statement “if not p, then not q”)
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Irregular polygon |
A polygon where all sides and angles are not congruent
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Isometric drawings |
Drawings on isometric dot paper used to show 3-dimensional objects
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Isosceles triangle |
A triangle with at least two sides congruent
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L |
Line of symmetry
| The line over which a figure is reflected resulting in a figure that coincides exactly with the original figure
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Linear pair of angles
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Two adjacent angles form a linear pair if their non-shared rays form a straight angle.
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M |
Matrix logic |
Using a matrix to solve logic problems
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Median of a triangle
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A segment that has as its endpoints a vertex of the triangle and the midpoint of the opposite side
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Midpoint of a segment |
The point that divides a segment into two congruent segments |
Midsegment
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A segment whose endpoints are the midpoints of two sides of a polygon
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O |
Orthocenter |
The orthocenter is the point of concurrency of the altitudes of a triangle.
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Orthographic drawings |
An orthographic drawing is the top view, front view and right side view of a three-dimensional figure.
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P |
Parallel lines |
Lines in a plane that never intersect
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Parallelogram |
A quadrilateral with both pairs of opposite sides parallel
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Perimeter |
The distance around a polygon
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Perpendicular bisector
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The perpendicular bisector of a segment is a line, segment or ray that is perpendicular to the segment at its midpoint.
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Perpendicular |
Two lines, segments, rays, or planes that intersect to form right angles
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Planes |
A flat surface having no boundaries
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Platonic solid
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A polyhedron all of whose faces are congruent regular polygons, and where the same number of faces meet at every vertex
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Point |
A specific location in space
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Polygon
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A closed plane figure whose sides are segments that intersect only at their endpoints with each segment intersecting exactly two other segments
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Postulates |
A mathematical statement that is accepted without proof
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Prism
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A three-dimensional figure--with two congruent faces called bases--that lies in parallel planes
(The other faces called lateral faces are rectangles that connect corresponding vertices of the bases.)
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Pyramid
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A three-dimensional figure with one base that is a polygon (The other faces, called lateral faces, are triangles that connect the base to the vertex.)
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Q |
Quadrilateral |
A four-sided polygon
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R |
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Radius |
A line segment having one endpoint at the center of the circle and the other endpoint on the circle
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Reflections |
Mirror images of a figure (Objects stay the same shape, but their positions change through a flip.)
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Regular octagon |
An octagon with all sides and angles congruent
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Regular polygon |
A polygon with all sides and angles congruent
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Rotations |
A transformation in which every point moves along a circular path around a fixed point called the center of rotation
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S |
Scale drawings |
Pictures that show relative sizes of real objects
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Secants
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A line, ray or segment that intersects a circle at two points
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Similarity |
The property of being similar
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Similar polygons
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Two polygons are similar if corresponding angles are congruent and the lengths of corresponding sides are in proportion.
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Sine
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In a right triangle, the ratio of the length of the leg opposite the angle to the length of the hypotenuse |
Slope |
The ratio of the vertical change to the horizontal change
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Slope-intercept form
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A linear equation in the form y = mx + b, where m is the slope of the graph of the equation and b is the y intercept
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Special right triangles
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A triangle whose angles are either 30-60-90 degrees or 45-45-90 degrees
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Spheres
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The set of all points in space equal distance from a given point
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Standard form of an equation
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The form of a linear equation Ax + By = C where A, B, and C are real numbers and A and C are not both zero Ex. 6x + 2y = 10
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Supplementary angles |
Two angles whose measures add up to 180 degrees |
Surface area |
The area of a net for a three-dimensional figure
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T |
Tangent |
In a right triangle, the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle
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Tangent to a circle
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A line in the plane of the circle that intersects the circle in only one point
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Tessellate
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A pattern of polygons that covers a plane without gaps or overlaps
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Theorems |
A conjecture that can be proven to be true
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Transformation |
A change made to the size or position of a figure
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Translation |
A transformation that slides each point of a figure the same distance in the same direction
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Transversal
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A line that intersects two or more other lines in the same plane at different points
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Triangle Inequality Theorem |
The sum of the lengths of any two sides of a triangle is greater than the lengths of the third side.
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Trigonometric ratios |
The sine, cosine and tangent ratios |
V |
Venn diagram |
A display that pictures unions and intersections of sets
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Vertical angles |
Non-adjacent, non-overlapping congruent angles formed by two intersecting lines (They share a common vertex.)
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/ 1 and / 3 are vertical angles.
/ 2 and / 4 are vertical angles. |
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Volume |
The number of cubic units needed to fill a space |
