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| a zero-dimensional figure; while usually left undefined, has four main representions - the dot, the node, the location, and the ordered pair of numbers |
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| a two-dimensional object that has no endpoints and continues on forever in a plane; formed of infinite points; the 3 orientations that lines may have are horizontal, vertical, oblique, and skew lines |
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| a two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines |
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| a polygonal region of a surface |
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| a segment that helps to make up a face |
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| A straight line which links two points without extending beyond them. |
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| a one-dimensional figure that consists of one endpoint A, one point B, all of the points on , and all points for which B is between them and A |
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| non-coplanar lines that don't intersect |
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| he union of 2 rays that have the same endpoint; measured in degrees or radians (trig.); the five types of angles are zero, acute, right, obtuse, and straight |
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| an angle less than 90 degrees |
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| an angle exactly 90 degrees |
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| and angle greater than 90 degrees but smaller than 180 degrees |
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| an angle exactly 180 degrees |
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| a ray that is in the interior of an angle and forms two equal angles with the sides of that angle |
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| the point M of where AM = AB |
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| 2 nonstraight and nonzero angles that have a common side in the interior of the angle formed by the noncommon sides |
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| 2 angles that share a common vertex and whose sides form 2 lines |
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| 2 supplementary adjacent angles whose noncommon sides form a line |
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| 2 angles whose measures, when added together, equal 90 degrees; see supplementary angles |
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| 2 angles whose measures, when added together, equal 180 degrees |
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| two lines that never touch |
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| 2 segments, rays, or lines that form a 90 degree angle |
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| equilateral, equal, exactly the same (size, shape, etc.) |
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| a transformation that keeps the same size and shape of a figure but moves it to a new location; see reflection, rotation, translation, glide reflection |
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| A drawing that represents a three dimensional object by showing separate drawings for the front, top and right side views |
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| a 2-D figure that can be folded on its segments or curved on its boundaries to form a 3-D figure |
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| a 3-d figure made up of squares |
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| the surface of a cylindric solid whose base is a circle |
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| the surface of a conic solid whose base is a circle |
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| the surface of a cylindric solid whose base is a polygon; see right prism, parallelpiped, box |
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| the surface of a conic solid whose base is a polygon; see regular pyramid |
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| the set of points in space equidistant from a certain point |
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| a three-dimensional surface which is the union of polygonal regions and has no holes |
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There are five Platonic Solids.
Each one is a polyhedron with every face being a regular polygon of the same size and shape. |
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| an educated guess or opinion; a hypothesis |
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| a statement assumed to be true without proof; see theorem |
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| a statement assumed to be true without proof |
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| a statement that tells if one thing happens, another will follow; written as pq; see antecedent, consequent, converse, inverse, contrapositive |
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| the side opposite the right angle in a right triangle |
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| he outcome or result of an act, process, event, |
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| a reversed conditional; if a conditional is pq, than its converse is qp |
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| a form of conditional; if not p, then not q; written ~p~q |
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| a type of conditional; if not q, then not p; written ~q~p; see inverse |
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| a conditional and its converse where the converse is also true; uses the words if and only if; written pq |
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| a situation in a conditional for which the antecedent is true, but the conditional is false; aka contradiction |
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| When we arrive at a conclusion using facts, definitions, rule, or properties, it is called Deductive Reasoning. |
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| Mathematical Induction is a method generally used to prove or establish that a given statement is true for all natural numbers. |
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| a precise way of drawing which allows only 2 tools: the straightedge and the compass |
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| the distance between points A and B is written as AB |
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x2 and y2 are the x,y coordinates for one point
x1and y1 are the x,y coordinates for the second point
d is the distance between the two points |
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| the measure of the tilt of a line; rise over run (i.e., how much the line moves up for every movement to the right). The formula for slope is |
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| (x1+x2/y1+y2)(x1+x2/y1+y2) |
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| A line that cuts across two or more (usually parallel) lines. |
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| any pair of angles in similar locations with respect to a transversal |
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| exterior angles on alternate sides of the transversal (not on the same parallel line) |
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| angles between two lines cut by a transversal; see exterior angles |
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| Exterior Angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on the same side of the transversal. |
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| Created where a transversal crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal. |
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| A right triangle is triangle with an angle of ( radians). The sides , , and of such a triangle satisfy the Pythagorean theorem |
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| An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A triangle must be either obtuse, acute, or right. |
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| A triangle where all three internal angles are acute (less than 90 degrees). |
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| a triangle whose sides are equal in length |
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| a triangle with two sides of equal length |
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| a triangle with no equilateral sides |
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The point where three or more lines intersect.
(Usually refers to various centers of a triangle). |
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The point where the three perpendicular bisectors of a triangle meet.
One of a triangle's points of concurrency. |
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| A geometric figure that is drawn around another geometric figure so as to touch all its vertices is called Circumscribed. |
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The point where the three angle bisectors of a triangle meet.
One of a triangle's points of concurrency. |
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| The angle subtended at a point on the circle by two given points on the circle. |
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The point where the three medians of the triangle intersect.
The 'center of gravity' of the triangle
One of a triangle's points of concurrency. |
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| the segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it |
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The point where the three altitudes of a triangle intersect.
One of a triangle's points of concurrency. |
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| a polygon with three sides; see equilateral triangle, isoscoles triangle, right triangle, scalene triangle |
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| t is intended as an easy way to remember that when you have two triangles and you have proved they are congruent, then each part of one triangle (side, or angle) is congruent to the corresponding part in the other. |
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| Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other. |
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| Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. |
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| Triangles are congruent if any two angles and their included side are equal in both triangles. |
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| Click on the "other triangle" under the triangle on the right. |
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| Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. |
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| a triangle that is angled |
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| Two polygons are similar polygons if corresponding angles have the same measure and corresponding sides are in proportion. |
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| Two polygons are similar polygons if corresponding angles have the same measure and corresponding sides are in proportion. |
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| Ratio is a concept that you have probably encountered in other math classes. It is a comparison of sizes. |
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| The mean proportional of two positive numbers a and b is the positive number x such that . When solving, . |
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| the angle made by two sides of a polygon |
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| A triangle where one of its interior angles is a right angle (90 degrees). |
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In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
A2+B2=C2 |
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| A right triangle where the sides are in the ratio of integers. (Integers are whole numbers like 3, 12 etc) |
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Sin=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent |
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| The angle subtended at the center of a circle by two given points on the circle. |
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| The perpendicular distance from the center of a regular polygon to any of its sides. |
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| Numbers which follow each other in order, without gaps, from smallest to largest. |
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| A polyhedron whose faces are identical regular polygons. |
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| A quadrilateral with both pairs of opposite sides parallel. |
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| A 4-sided polygon where all interior angles are 90° |
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| : A quadrilateral with all four sides equal in length. |
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| A 4-sided regular polygon with all sides equal and all internal angles 90° |
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| A quadrilateral which has at least one pair of parallel sides |
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| A quadrilateral with two distinct pairs of equal adjacent sides. |
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| A solid object that has two identical ends and all flat sides. |
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Prism
A solid object that has two identical ends and all flat sides. |
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| A solid (3-dimensional) object that has a circular base and one vertex |
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| A line forming a closed loop, every point on which is a fixed distance from a center point. |
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| A secant is a line that intersects a circle at two points |
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| A line that links two points on a circle or curve. (pronounced "cord") |
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| A line which touches a circle or ellipse at just one point. Below, the blue line is a tangent to the circle c. Note the radius to the point of tangency is always perpendicular to the tangent line. |
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| Half a circle. A closed shape consisting of half a circle and a diameter of that circle*. |
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| Given two points on a circle, the minor arc is the shortest arc linking them. The major arc is the longest. |
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| Given two points on a circle, the minor arc is the shortest arc linking them. The major arc is the longest. |
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| The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle. |
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| The distance along the curved line making up the arc |
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| The angle subtended at a point on the circle by two given points on the circle. |
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