Download Geometry Concepts VOCABULARY

Geometry Vocabulary
Chapter 1
Undefined Terms: words like point, line, and plane that are words that have no formal
definitions, but there is agreement about what they mean.
Point: has no dimension, represented by a dot.
Line: has one dimension. It is represented by a line with two arrowheads, but extends without
end. Through any two points there is exactly one line.
Plane: has two dimensions. It is represented by a shape that looks like a floor or a wall, but it
extends without end. Through any three points not on the same line, there is exactly one plane.
Collinear Points: points that lie on the same line.
Coplanar Points: points that lie on the same plane.
Defined Terms: terms that can be described using known words such as point and line.
Segment: the line segment AB, or segment AB, (written as 𝐴𝐵) consists of the endpoints A and B
and all points on ⃡𝐴𝐵 (line ⃡𝐴𝐵 ) that are between A and B.
Ray: the ray AB (written as 𝐴𝐵 ) consists of the endpoint A and all points on ⃡𝐴𝐵 that lie on the
same side of A as B.
Opposite Rays: If point C lies on ⃡𝐴𝐵 between A and B, then 𝐶𝐴 and 𝐶𝐵 are opposite rays.
Intersection: between two figures, is the set of points the figures have in common.
Postulate: a rule that is accepted without proof, also called an axiom.
Coordinate: the real number the corresponds to a point on a line.
Distance: between points A and B is the absolute value of the difference of the coordinates A and
B
Between: when three points are collinear, you can say that one point is between the other two.
Congruent Segments: line segments that have the same length.
Midpoint: is the point that divides the segment into two congruent segments.
Segment Bisector: a point, ray, line segment, or plane that intersects the segment at its midpoint.
Angle: consists of two different rays with the same endpoint.
Sides: the rays of the angle
Vertex: the endpoint of the angle
Measure of an Angle: the number of degrees the angle opens to.
Acute Angle: classification of an angle when the measure of the angle is between 0° and 90°.
Right Angle: classification of an angle when the measure of the angle is exactly 90°.
Obtuse Angle: classification of an angle when the measure of the angle is between 90° and 180°.
Straight Angle: classification of an angle when the measure of the angle is exactly 180°.
Congruent Angles: when angles have the same measure.
Angle Bisector: a ray that divides an angle into two angles that are congruent.
Complementary Angles: when the sum of two angle measures is equal to 90°.
Supplementary Angles: when the sum of two angle measures is equal to 180°.
Adjacent Angles: two angles that share a common vertex and side, but have no common interior
points.
Linear Pair: two adjacent angles are this is their non-common sides are opposite rays. The
angles in a linear pair are supplementary angles.
Vertical Angles: two angles are this if their sides form two pairs of opposite rays
Chapter 2
Conjecture: an unproven statement that is based on observations.
Inductive Reasoning: when you find a pattern in specific cases then write a conjecture for the
general case.
Counterexample: a specific case for which a conjecture is false.
Conditional Statement: a logical statement that has two parts, a hypothesis and a conclusion.
If-Then Form: when a conditional statement is written with the if part having the hypothesis and
the then part having the conclusion.
Negation: the opposite of the original statement.
Converse Statement: the conditional statement with the hypothesis and the conclusion switched.
Inverse Statement: negation of both the hypothesis and the conclusion of the conditional
statement.
Contrapositive Statement: write the converse statement then negate both the hypothesis and the
conclusion.
Perpendicular Lines: when two lines intersect to form a right angle.
Biconditional Statement: a statement that contains the phrase “If and only if”. Any definition
can be written as a biconditional statement
Deductive Reasoning: uses facts, definitions, accepted properties, and the laws of logic to form
a logical argument.
Line Perpendicular to a Plane: a ling is this if and only if the line intersects the plane in a point
and is perpendicular to every line in the plan that intersects it at that point.
Proof: a logical argument that shows a statement is true.
Two-Column Proof: has numbered statements and corresponding reasons that show an
argument in a logical order.
Theorem: is a statement that can be proven. Once a theorem is proven, it can be used in other
proofs.
Chapter 3
Parallel Lines: lines that do not intersect and are coplanar.
Skew Lines: lines that do not intersect and are not coplanar.
Parallel Planes: two planes that do not intersect.
Transversal: is a line that intersects two or more coplanar lines at different points
Corresponding Angles: two angles are this is they have corresponding positions.
Alternate Interior Angles: two angles are this if they lie between the two lines and on opposite
sides of the transversal.
Alternate Exterior Angles: Two angles are this if they lie outside the two lines and on opposite
sides of the transversal.
Consecutive Interior Angles: two angles are this if they lie between the two lines and on the
same side of the transversal.
Paragraph Proof: a proof written in paragraph form using sentences with words to explain the
logical flow of the argument.
Slope: the ratio of the vertical change to the horizontal change between any two points on the
line.
Slope-Intercept Form: the general linear equation, 𝑦 = 𝑚𝑥 + 𝑏, where m is the slope and b is
the y-intercept.
Standard Form: another form of a linear equation, written as 𝐴𝑥 + 𝐵𝑦 = 𝐶, where A and B are
not both zero.
Distance from a Point to a Line: the length of the perpendicular segment from the point to the
line.
Chapter 4
Triangle: a polygon with three sides. A triangle with vertices A, B, and C is called “triangle
ABC” or “∆𝐴𝐵𝐶”.
Interior Angles: these are the original angles when the sides of a polygon are extended.
Exterior Angles: these angles form linear pairs with the interior angles when the sides of a
polygon are extended.
Corollary to a Theorem: a statement that can be proved easily using the theorem.
Congruent Figures: all the parts of one figure are congruent to the corresponding parts of the
other figure.
Corresponding Parts: a pair of sides or angles that have the same relative position in two
congruent or similar figures.
Legs of a Right Triangle: the sides adjacent to the right angle.
Hypotenuse: the side opposite the right angle.
Flow Proof: uses arrows to show the flow of a logical argument
Legs of an Isosceles Triangle: exactly two congruent sides.
Vertex Angle: the angle formed by the legs.
Base: the third side of the isosceles triangle.
Base Angles: the angles adjacent to the base.
Transformation: is an operation that moves or changes a geometric figure in some way to
produce a new figure
Image: the new figure produced by the operation
Translation: moves every point of the figure the same distance in the same direction.
Reflection: uses a line of reflection to create a mirror image of the original figure.
Rotation: turns a figure about a fixed point, the center of rotation.
Congruence Transformation: changes the position of the figure without changing its size or
shape.
Chapter 5
Midsegment of a Triangle: a segment that connects the midpoints of two sides of the triangle.
Coordinate Proof: involves placing geometric figures in a coordinate plane.
Perpendicular Bisector: a segment, ray, line, or plane that is perpendicular to a segment at its
midpoint.
Equidistant: when a point is the same distance from each figure.
Concurrent: when three or more lines, rays, or segments intersect in the same point.
Point of Concurrency: the point of intersection of the lines, rays, or segments.
Circumcenter: the point of concurrency of the three perpendicular bisectors of a triangle.
Incenter: the point of concurrency of the three angle bisectors of a triangle.
Median of a Triangle: a segment from a vertex to the midpoint of the opposite side.
Centroid: the point of concurrency inside the triangle.
Altitude of a Triangle: the perpendicular segment from a vertex to the opposite side or to the
line that contains the opposite side.
Orthocenter: the point at which the lines containing the three altitudes of a triangle intersect.
Indirect Proof: you start by making the temporary assumption that the desired conclusion is
false. Then show that this assumption leads to a logical impossibility, this proves the original
statement true by contradiction.
Chapter 6
𝑎
Ratio of a to b: if a and b are two numbers or quantities and b ≠ 0, the ratio is 𝑏.
Proportion: an equation that states two ratios are equal.
𝑎
𝒄
Means: the numbers b and c of the proportion: 𝒃 = 𝑑
𝒂
𝑐
Extremes: the numbers a and d of the proportion: 𝑏 = 𝒅.
𝑎
𝒙
Geometric Mean: of two positive numbers a and b is the positive number x that satisfies 𝒙 = 𝑏.
So, 𝒙2 = ab and x = √𝑎𝑏.
Scale Drawing: is a drawing that is the same shape as the object it represents.
Scale: a ratio that describes how the dimensions in the drawing are related to the actual
dimensions of the object.
Similar Polygons: corresponding angles are congruent and corresponding side lengths are
proportional.
Scale Factor: when two polygons are similar, this is the ratio of the lengths of two
corresponding sides.
Dilation: a transformation that stretches or shrinks a figure to create a similar figure. A type of
similarity transformation.
Center of Dilation: in a dilation, a figure is enlarged or reduced with respect to a fixed point.
Scale Factor of a Dilation: the ratio of a side length of the image to the corresponding side
length of the original figure.
Reduction: if the dilation is 0 < 𝑘 < 1, where k is the scale factor.
Enlargement: if the dilation is 𝑘 > 1, where k is the scale factor.
Chapter 7
Pythagorean Triple: a set of three positive integers a, b, and c that satisfy the equation
𝑐 2 = 𝑎2 + 𝑏 2 .
Trigonometric Ratio: a ratio of the lengths of two sides in a right triangle.
Tangent: the ratio of the lengths of the legs in a right triangle is constant for a given angle
measure.
Sine: trigonometric ratios of the length of leg opposite of length of hypotenuse.
Cosine: trigonometric ratio of the length of leg adjacent to length of hypotenuse.
Angle of Elevation: if you look up at an object, the angle your line of sight makes with a
horizontal line.
Angle of Depression: if you look down at an object, the angle your line of sight makes with a
horizontal line
Solve a Right Triangle: means to find the measures of all of its sides and angles. You can solve
a right triangle if you know either two side lengths of one side length and the measure of one
acute angle.
Chapter 8
Diagonal: a segment that joins two nonconsecutive vertices
Parallelogram: a quadrilateral with both pairs of opposite sides parallel.
Rhombus: a parallelogram with four congruent sides.
Rectangle: a parallelogram with four right angles.
Square: a parallelogram with four congruent sides and four right angles.
Trapezoid: a quadrilateral with exactly one pair of parallel sides.
Bases: the parallel sides of a trapezoid.
Base Angles: a trapezoid has two pairs of these angles.
Legs of a Trapezoid: the nonparallel sides of the trapezoid.
Isosceles Trapezoid: if the legs of a trapezoid are congruent.
Midsegment of a Trapezoid: is the segment that connects the midpoints of its legs.
Kite: a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not
congruent.
Chapter 9
Image: when a transformation moves or changes a figure in some way to produce a new figure.
Preimage: another name for the original figure.
Isometry: a transformation that preserves length and angle measure.
Vector: is a quantity that has both direction and magnitude, or size.
Initial Point: the starting point of the vector.
Terminal Point: the ending point of a vector.
Component Form: combines the horizontal and vertical components.
Matrix: a rectangular arrangement of numbers in rows and columns.
Element: each number in a matrix
Dimensions: are the numbers of rows and columns.
Line of Reflection: the mirror line that reflects and image.
Center of Rotation: a rotation is a transformation in which a figure is turned about a fixed point
Angle of Rotation: rays drawn from the center of rotation to a point and its image.
Glide Reflection: a transformation in which every point P is mapped to a point P”, by the
following steps: Step 1 – A translation maps P to P’. Step 2 – A reflection in a line k parallel to
the direction of the translation maps P’ to P”.
Composition of Transformation: when two or more transformations are combined to form a
single transformation.
Line Symmetry: a figure in the plane has this if the figure can be mapped onto itself by a
reflection in a line.
Line of Symmetry: line of reflection for a figure to map onto itself.
Rotational Symmetry: a figure in a plane has this if the figure can be mapped onto itself by a
rotation of 180° or less about the center of the figure.
Center of Symmetry: the point at which the rotation of the figure happens.
Scalar Multiplication: the process of multiplying each element of a matrix by a real number or
a scalar.
Chapter 10
Circle: the set of all points in a plane that are equidistant from a given point.
Center: the middle point that all points of a circle are equidistant from.
Radius: a segment whose endpoints are the center and any point on the circle.
Chord: is a segment whose endpoints are on a circle.
Diameter: a chord that contains the center of the circle.
Secant: is a line that intersects a circle in two points.
Tangent: a line in a plane of a circle that intersects the circle in exactly one point, the point of
tangency.
Central Angle: is an angle whose vertex is the center of the circle.
Minor Arc: if m𝐴𝐵𝐶 is less than 180°, then the points on circle C that lie in the interior of
𝐴𝐵𝐶 form the minor arc.
̂ form the major arc.
Major Arc: the points on circle C that do not lie on minor arc 𝐴𝐵
Semicircle: an arc with endpoints that are the endpoints of a diameter.
Measure of Minor Arc: the measure of the central angle.
Measure of a Major Arc: the difference between 360° and the measure of the related minor arc.
Congruent Circles: congruent if they have the same radius.
Congruent Arcs: congruent if they have the same measure and they are arcs of the same circle
or of congruent circles.
Inscribed Angle: an angle whose vertex is on a circle and whose sides contains chords of the
circle.
Intercepted Arc: the arc that lies in the interior of an inscribed angle and has endpoints on the
angle.
Inscribed Polygon: a polygon that has all of its vertices lying on a circle.
Circumscribed Circle: the circle that contains the vertices.
Segments of the Chord: when two chords intersect in the interior of a circle, each chord is
divided into two segments.
Secant Segment: a segment that contains a chord of a circle, and has exactly one endpoint
outside the circle.
External Segment: the part of a second segment that is outside the circle.
Standard Equation of a Circle: the standard equation of a circle with center (h, k) and radius r
is (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
Chapter 11
Bases of a Parallelogram: either pair of parallel sides.
Height of a Parallelogram: the perpendicular distance between these bases.
Height of a Trapezoid: the perpendicular distance between its bases.
Circumference: is the distance around the circle.
Arc Length: is a portion of the circumference of a circle.
Sector of a Circle: the region bounded by two radii of the circle and the intercepted arc.
Center of the Polygon: the center of its circumscribed circle.
Radius of the Polygon: the radius of the circumscribed circle.
Apothem of the Polygon: the distances from the center to any side of the polygon.
Central Angle of a Regular Polygon: an angle formed by two radii drawn to consecutive
vertices of the polygon.
Probability: is a measure of the likelihood that the event will occur.
Geometric Probability: a ratio that involved a geometric measure such as length or area.
Chapter 12
Polyhedron: a solid that is bounded by polygons.
Faces: the planes that enclose a single region of space.
Edge: a line segment formed by the intersection of two faces.
Vertex: a point where three or more edges meet.
Regular Polyhedron: all of its faces are congruent regular polygons.
Convex Polyhedron: any two points on its surface can be connected by a segment that lies
entirely inside or on the polyhedron.
Platonic Solids: there are five regular polyhedral, regular tetrahedron, cube, regular octahedron,
regular dodecahedron, regular icosahedron.
Cross Section: the intersection of the plane and the solid.
Prism: a polyhedron with two congruent faces that lie in parallel planes.
Lateral Faces: the other faces are parallelograms formed by connecting the corresponding
vertices of the bases.
Lateral Edges: the segments connecting these vertices.
Surface Area: the sum of the areas of its faces.
Lateral Area: the sum of the areas of its lateral faces.
Net: the two-dimensional representation of the faces.
Right Prism: each lateral edge is perpendicular to both bases.
Oblique Prism: a prism with lateral edges that are not perpendicular to the bases.
Cylinder: a solid with congruent circular bases that lie in parallel planes.
Right Cylinder: the segment joining the centers of the bases is perpendicular to the bases.
Pyramid: a polyhedron in which the base is a polygon and the lateral faces are triangles with a
common vertex.
Vertex of the Pyramid: the common vertex between the lateral faces.
Regular Pyramid: a regular polygon for a base and the segment joining the verte and the center
of the base is perpendicular to the base.
Slant Height: the height of a lateral face of the regular pyramid.
Cone: has a circular base and a vertex that is not in the same plane as the base.
Right Cone: the segment joining the vertex and the center of the base is perpendicular to the
base, and the slant height is the distance between the vertex and a point on the base edge.
Lateral Surface: consists of all segments that connect the vertex with points on the base edge.
Volume: the number of cubic units contained in its interior.
Sphere: the set of all points in space equidistant from a given point.
Center: the point that all points in space are equidistant from.
Radius of a Sphere: a segment from the center to a point on the sphere
Chord of a Sphere: a segment whose endpoints are on the sphere.
Diameter of a Sphere: a chord that contains the center.
Great Circle: if the plane contains the center of the sphere, then the intersection is a great circle
Hemispheres: every great circle of a sphere separates the sphere into two congruent halves.
Similar Solids: two solids of the same type with equal ratios of corresponding linear measures,
such as heights or radii.