Geometry
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Altitude of a triangle | A straight line through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side) of a triangle
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| Angle bisector theorem | Concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
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| Arc | A closed segment (symbol: ⌒) of a differentiable curve in the two-dimensional plane
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| Area | Any particular extent of space or surface. A=L*W (Always write area in #measure squared).
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| Center of a polygon | In a rotation, the point that does not move. The rest of the plane rotates around this one fixed point.
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| Centroid of a triangle | The point where the three medians of the triangle intersect
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| Circumcenter of a triangle | The point where the three perpendicular bisectors of a triangle meet
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| Circumference (circles) | A complete circular arc; also the distance around the outside of a circle. C=Pi*r(r).
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| Circumscribed | A geometric figure that is drawn around another geometric figure so as to touch all its vertices
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| Combination | A way of selecting several things out of a larger group, where (unlike permutations) order does not matter.
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| Compass | An instrument for drawing circles and arcs and measuring distances between points, consisting of two arms linked by a movable joint.
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| Composition | The combining of distinct parts or elements to form a whole
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| Compound event | An event whose probability of occurrence depends upon the probability of occurrence of two or more independent events
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| Compression | To reduce a shape in size while retaining proportions
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| Conditional probability | The probability that an event will occur, when another event is known to occur or to have occurred
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| Conditional probability formula | The conditional probability of A given B is denoted by P(A|B) and defined by the formula P(A|B) = P(AB) P(B), provided P(B) > 0.
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| Dependent events | When the outcome of one event affects the outcome of another.
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| Dilation | A transformation that grows or shrinks a polygon by a given proportion about a center point
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| Events | A set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned
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| Experimental probability | The ratio of the number of times the event occurs to the total number of trials
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| Frequency table | Lists items and uses tally marks to record and show the number of times they occur
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| Fundamental counting principle | When there are m ways to do one thing, and n ways to do another, then there are m×n ways of doing both.
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| Glide reflection | A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation
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| Glide reflectional symmetry | The symmetry that a figure has if it can be made to fit exactly onto the original when it is translated a given distance at a given direction and then reflected over a line.
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| Hypotenuse-leg theorem (HL theorem) | If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
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| Image | An optically formed duplicate, counterpart, or other representative
reproduction of an object, especially an optical reproduction formed by a lens or mirror
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| Incenter of a triangle | The point where the three angle bisectors of a triangle meet
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| Included angle | The angle made by two lines with a common vertex
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| Independent events | When the outcome of one event does not influence the outcome of thesecond event
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| Inscribed in (the triangle) | Drawing one shape inside a triangle so that it just touches the sides of the triangle
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| Intersection | The probability that events A and B both will occur
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| Isometry | A transformation that is invariant with respect to distance. That is, the distance between any two points in the pre-image must be the same as the distance between the images of the two points.
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| Median of a triangle | A line segment joining a vertex of a triangle to the midpoint of the opposing side
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| Midsegment of a triangle | The segment joining the midpoints of two sides of a triangle
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| Mutually exclusive events | Two events that cannot occur at the same time
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| n factorial | The factorial of a natural number n is the product of the positive integers less than or equal to n.
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| Non-included angle | The side of a triangle that is not included by two given angles
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| Ordered triple | Three numbers written in the form (x, y, z)
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| n-tuple | n numbers written in the form (x1, x2, x3, . . . , xn)
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| Orthocenter of a triangle | The point where the three altitudes of a triangle intersect
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| Overlap | Similar triangles in which one triangle is on top of (overlapping) another
triangle
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| Permutation | All possible arrangements of a collection of things, where the order is important
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| Point of symmetry | A special center point for certain kinds of symmetric figures or graphs. If a figure or graph can be rotated 180° about a point P and end up looking identical to the original, then P is a point of symmetry.
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| Polygon angle-sum theorem, corollary | The measure of each interior angle of a regular n-gon is 180*(n–2)/n)
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| Polygon exterior angle-sum theorem | If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360.
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| Preimage | The original figure prior to a transformation.
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| Probability distribution | A graph, table, or formula that gives the probability for each value of the random variable
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| Probability formula | The number of ways an event can occur divided by the total number of possible outcomes
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| Relative frequency | The ratio of the actual number of favorable events to the total possible
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| Remote interior angles | The two angles of a triangle that are not adjacent to the exterior angle, which is drawn by extending one of the sides.
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| Rigid motion | The variance in position and orientation when a rigid body moves
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| Sample space | In probability theory, the set of all possible outcomes or results of an experiment
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| Tessellation | A plane with identically shaped pieces that do not overlap or leave blank spaces. The pieces do not have to be oriented identically. A tessellation may use tiles of one, two, three, or any finite number of shapes.
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| Theoretical probability | The likelihood of an event happening based on all the possible outcomes
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| Transformation | Operations that alter the form of a figure. The standard transformations are translations, reflections, dilations (stretches), compressions (contractions or shrinks), and rotations.
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| Tree diagram | A representation of a tree structure in which the probability of each branch is written on the branch and the outcome is written at the end of the branch
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| Volume (prisms, cylinders, pyramids, cones, spheres) | The total amount of space enclosed in a solid. (Always write volume in #measure cubed).
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