Acute Angle An angle whose measure is less than 90°

Adjacent Angles Two angles with a common vertex and a common side.

Alternate Exterior Angles 2 and 8 1 and 7 Two non-adjacent angles that lie on the opposite sides of a transversal outside two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

Alternate Interior Angles 3 and 6 4 and 5 Two non-adjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

Angle Formed by 2 rays (sides) with the same endpoint (vertex). X 3 V Z 3  

Angle Addition Postulate If T is in the interior of ∠QRS, then m∠QRT + m∠TRS = m∠QRS.

Angle Bisector A ray that divides an angle into two congruent angles.  

Auxiliary Line A line (or ray or segment) added to a diagram to help in a proof or in determining the solution to a problem. DE is an auxiliary line.

Biconditional Two statements connected by the words “if and only if.”

Collinear Points that are on the same line. A B C D E A, B, C, and D are collinear points. A, B, C, D, and E are non-collinear points.

Complementary Two angles whose measures have a sum of 90.

Compound Statement A statement formed when two or more simple statements are connected as either a conditional (if-then), a biconditional (if and only if), a conjunction (and), or a disjunction (or).

Conclusion The “then” statement in an if-then statement.

Conditional Statement A statement that tells if one thing happens another will follow. Example: “If a polygon has three sides then it is a triangle.”

Congruent Exactly equal in size and shape. Congruent segments have the same length. Congruent angles have the same measure.

Congruent Angles Angles that have the same measure. W X  

Congruent Segments Segments that have the same length. J K L M  

Conjecture An educated guess, opinion, hypothesis.

Conjunction Two statements joined by the word and, represented by the symbol ^.

Contrapositive A version of a conditional statement formed by interchanging and negating both the hypothesis and conclusion of the statement.

Converse A version of a conditional statement formed by interchanging the hypothesis and conclusion of the statement.

Coplanar Lines Lines that are in the same plane.

Coplanar Points Points that are in the same plane. F A B E C D A, B, C, D, and E are coplanar points. A, B, C, D, E, and F are non-coplanar points.

Corresponding Angles 1 and 5 2 and 4 3 and 8 4 and 7 Two non-adjacent angles that lie on the same side of a transversal, in “corresponding” positions with respect to the two lines that the transversal intersects. If the lines are parallel, then the angles are congruent.

Counterexample An example that shows that a conjecture is not always true.

Deductive Reasoning The use of facts, definitions, rules and/or properties to prove that a conjecture is true.

Disjunction The symbol v represents a disjunction, you read it as “or.”

Distance Formula The distance between 𝑥 1, 𝑦 1 and 𝑥 2 , 𝑦 2 can be found using the formula 𝑥 2 − 𝑥 1 2 + ( 𝑦 2 − 𝑦 1 ) 2

Endpoint A point at one end of a segment or the starting point of a ray.

Hypothesis The “if” clause in an if-then statement.

Inductive Reasoning The process of observing data, recognizing patterns, and making a generalization.

Inverse A version of a conditional statement formed by negating both the hypothesis and conclusion of the statement.

Line A set of points that extends in 2 directions without end. m A B Line m or line AB or AB

Segment MN or Segment NM or MN or NM Line Segment Part of a line consisting of two endpoints and all points between them. N M Segment MN or Segment NM or MN or NM

Linear Pair A pair of adjacent angles whose noncommon side are opposite rays.  

Logically Equivalent When two statements have the same exact truth values.

Midpoint A point that divides a segment into two congruent segments. A B  

Midpoint Formula The midpoint of a segement with endpoints 𝑥 1, 𝑦 1 and 𝑥 2 , 𝑦 2 can be found using the formula 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2

Negation of p The symbol ~p is the negation of p and can be read as “not p.”

Obtuse Angle An angle whose measure is greater than 90° but less than 180°.

Opposite Rays Two collinear rays with the same endpoint. They always form a line. F H D HF and HD are opposite rays.

Parallel Lines Coplanar lines that do not intersect. a c a//c

Parallel Planes Planes that do not intersect. W M

Perpendicular Lines 2 lines intersect to form right angles. A C B  

Perpendicular Planes Planes intersect to form right angles. B D

Plane A flat surface that extends in all directions without end. It has no thickness. W A B C Plane W or Plane ABC

Point A location in space •A

Postulate A statement that is accepted without proof.

Proof An argument that transforms a conjecture to a theorem through the application of logical reasoning or deductive reasoning.

Pythagorean Theorem For sides a, b, and c in a right triangle, a2 + b2 = c2.

Pythagorean Triple Three integers a, b, and c such that a2 + b2 = c2

Ray Part of a line consisting of one endpoint and all points of the line on one side of the endpoint. R S RS not SR

Right Angle An angle whose measure is exactly 90°.

Same Side Exterior Angles 1 and 8 2 and 7 Two angles that lie on the same side of a transversal and outside the lines cut by the transversal. If the lines are parallel, then the angles are supplementary.

Same Side Interior Angles 3 and 5 4 and 6 Two angles that lie on the same side of a transversal and between the lines cut by the transversal. If the lines are parallel, then the angles are supplementary.

Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.

Segment Bisector A line, segment or ray that intersects a segment at its midpoint A C B  

Slope The ratio of the vertical change of a line to the horizontal change of the line.

Slope-Intercept Form A line with a slope m and y-intercept b can be written in the form y = mx + b.

Straight Angle An angle whose measure is exactly 180°.

Supplementary Two angles whose measures have a sum of 180.

Tautology A statement that is always true.

Theorem A result that has been proved to be true (using facts that were already known).

Transversal A line that intersects two or more coplanar lines at different points. Transversal

Truth Table Truth tables are used to determine the conditions under which a statement is true or false.

Truth Value The truth value of a statement is the truth or falsity of that statement.

Vertex The common endpoint of the sides of the angle. Vertex

Vertical Angles The non-adjacent angles formed by two intersecting lines.  

y-Intercept The y coordinate of the point where a graph intersects the y-axis.

AcuteTriangle A triangle with three acute angles.

Altitude of a Triangle A segment from a vertex and perpendicular to the opposite side or the line containing the opposite side.

Angle-Angle-Side (AAS) If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. ∠𝐵≅∠𝐸, ∠𝐶≅∠𝐹,𝐴𝐶≅𝐷𝐹,so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

Angle-Side-Angle (ASA) If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. ∠𝐵≅∠𝐸,𝐵𝐶≅𝐸𝐹, ∠𝐶≅∠𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

Apothem The perpendicular segment from the center of a regular polygon to the midpoint of a side.

Base Angles The two congruent angles in an isosceles triangle.

Bases (of a trapezoid) The parallel sides of a trapezoid.

Centroid The point where the medians of a triangle intersect.

Circumcenter The point where the three perpendicular bisectors of a triangle intersect. Circumcenter

Circumscribe To draw on the outside of, touching as many points as possible.

Circumscribed Circle A circle that contains all the vertices of a polygon.

Concave Polygon A polygon that has one or more interior angles that are greater than 180˚.

Congruent Triangle Two or more triangles whose side lengths and angle measures are congruent.  

Convex Polygon A polygon in which all interior angles have measures less than 180˚.

Corresponding Parts The angles, sides and vertices that are in the same location in congruent or similar figures.

Diagonal A segment that connects two non-consecutive vertices of a polygon. Diagonal

Equiangular A geometric figure in which all angles are equal.

Equilangular Triangle A triangle with three congruent angles.

Equilateral A geometric figure in which all sides are equal.

Equilateral Triangle A triangle with three congruent sides.

Exterior Angle The angle formed by extending a side of a polygon.

Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and then the larger third side is across from the larger included angle.

Hypotenuse-Leg (HL) If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent. 𝐴𝐶≅𝑍𝑌, 𝐴𝐵≅𝑍𝑋 so ∆𝐴𝐵𝐶 ≅∆𝑍𝑋𝑌

Incenter The point of concurrency of the angle bisectors of a triangle. Incenter

Interior Angle An angle inside a shape.

Isosceles Trapezoid A trapezoid with congruent legs.

Isosceles Triangle A triangle with two or more congruent sides and angles.

Kite A quadrilateral who two distinct pairs of adjacent congruent sides.

Legs (of a trapezoid) The nonparallel sides of a trapezoid.

Median of a Triangle A segment from a vertex to the midpoint of the opposite side.

Midsegment The segments whose endpoints are the midpoint of two sides of a triangle.

Obtuse Triangle A triangle with one obtuse angle.

Orthocenter The point where the three altitudes of a triangle intersect. Orthocenter

Parallelogram A quadrilateral in which both pairs of opposite sides are parallel and congruent. Opposite Angles are congruent and consecutive angles are supplementary.

Perpendicular Bisector of a Triangle A line or segment that is perpendicular to the side of a triangle at its midpoint. Perpendicular Bisector

Point of Concurrency The point where three or more lines intersect.

Polygon A closed plane figure formed by segments that only intersect at their endpoints.

Quadrilateral A polygon with four sides.

Rectangle A parallelogram with four right angles and congruent diagonals.

Regular Polygon A polygon that is both equilateral and equiangular.

Remote Interior Angles An interior angle in a polygon that is not adjacent to the exterior angle. In a triangle the sum of the two remote interior angles is equal to the exterior angle.

Rhombus A parallelogram with all sides congruent and diagonals that are perpendicular

Right Triangle A triangle with one right angle and two acute angles.

Scalene Triangle A triangle with no congruent sides.

Side-Angle-Side (SAS) If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. 𝐴𝐵≅𝐷𝐸,∠𝐵≅∠𝐸, 𝐵𝐶≅𝐸𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

Side-Side-Side (SSS) If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent. 𝐴𝐵≅𝐷𝐸, 𝐴𝐶≅𝐷𝐹,𝐵𝐶≅𝐸𝐹 so ∆𝐴𝐵𝐶 ≅∆𝐷𝐸𝐹

Square A parallelogram with all sides congruent and four right angles. A square has all the properties of a rectangle and a rhombus.

Trapezoid A quadrilateral with exactly one pair of parallel sides.

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Adjacent Leg The leg that is closest to the included angle in a right triangle.

Angle-Angle Similarity (AA~) In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar. ∠𝐴 ≅∠𝑃 and ∠𝐵 ≅∠𝑄 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

Angle Bisector Proportionality Theorem An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Constant of Proportionality The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality

Cosecant The cosecant of an acute angle in a right triangle is the ratio of the length of the hypotenuse to the length of the opposite side.

Cosine The cosine of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Cotangent The cotangent of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the opposite side.

Geometric Mean  

Opposite Leg The leg that is across from the included angle in a right triangle.

Parallel Proportionality Theorem If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. 𝑣∥𝑡∥𝑥 so 𝐴𝐵 𝐵𝐶 = 𝐷𝐸 𝐸𝐹 , 𝐴𝐶 𝐴𝐵 = 𝐷𝐹 𝐷𝐸 , 𝐴𝐶 𝐵𝐶 = 𝐷𝐹 𝐸𝐹

Secant The secant of an acute angle in a right triangle is the ratio of the length of the hypotenuse to the length of the adjacent side.

Side-Angle Side Similarity (SAS~) If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar. 𝐴𝐶 𝑃𝑅 = 𝐵𝐶 𝑄𝑅 and ∠𝐶≅∠𝑅 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

Side-Side-Side Similarity (SSS~) If the corresponding sides of two triangles are proportional, then the two triangles are similar. 𝐴𝐶 𝑃𝑅 = 𝐵𝐶 𝑄𝑅 = 𝐴𝐵 𝑃𝑄 so ∆𝐴𝐵𝐶 ~∆𝑃𝑄𝑅

Similar Polygon Polygons with congruent corresponding angles and corresponding side lengths in proportion.

Sine The sine of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

Special Right Triangle 30-60-90 and 45-45-90 are called special right triangles because they have some regular feature that makes calculations on the triangle easier.

Tangent The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

Triangle Proportionality Theorem If two or more lines parallel to a side of a triangle intersect the other two sides of the triangle, then they divide them proportionally. 𝐴𝐶 𝐶𝐸 = 𝐴𝐵 𝐵𝐷

Angles formed by Chords If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. 𝑚∠1=1/2(𝑚 𝑃𝑄 +𝑚 𝑅𝑆)

Angles formed by Secants If two secant segments intersect outside a circle, then the measure of the angle formed is one half the difference of the measure of the intercepted arcs. 𝑚∠𝐸=1/2(𝑚 𝐶𝐷 −𝑚 𝐵𝐴)

Angles formed by Tangents If two tangent segments intersect outside a circle, then the measure of the angle formed is one half the difference of the measure of the intercepted arcs. 𝑚∠𝐶=1/2(𝑚 𝐴𝐸𝐵 −𝑚 𝐵𝐴)

Arc A continuous part of a circle. The measure of the arc is the measure of the angle formed by the two radii with endpoints at the endpoints of the arc.

Central Angle An angle whose vertex is at the center of a circle and whose sides are radii of the circle Central Angle

Chords A line segment on the interior of a circle with both endpoints lying on the circle.  

Circle The set of all points in a plane that are a given distance (the radius) from a given point (the center) in the plane.

Congruent Arc Arcs of a circle that have the same length.

Diameter A chord that contains the center of the circle

Equation of a Circle The equation of a circle with center (h,k) and radius r is (x – h)2 + (y – k)2 = r2

External Secant Segment The parts of a secant segments that are outside the circle. EF and EH are external secant segments

Inscribed Angle An angle whose vertex is on the circle and whose sides are chords of the circle. Inscribed Angle

Major Arc An arc with a measure greater than 180˚.

Minor Arc An arc with a measure less than 180˚.

Point of Tangency The point where the tangent line intersects a circle. A radius is perpendicular the tangent at the point of tangency.

Radius A segment from the center of a circle to a point on the circle.

Secant Line/Segment A line/segment that intersects a circle exactly twice.

Sector A region formed by two radii and an arc of a circle.

Segments Lengths in Circles formed by Chords If two chords of a circle intersect, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. 𝑃𝐴∙𝑃𝐷=𝑃𝐶∙𝑃𝐵

Segments Lengths in Circles formed by Secants If two secants intersect at a point outside a circle, the product of one secant segment and its external secant segment equals the product of the other secant segment and its external secant segment. 𝑃𝐴∙𝑃𝐷=𝑃𝐶∙𝑃𝐵

Segments Lengths in Circles formed by a Secant and a Tangent If a secant and a tangent intersect at a point outside a circle, the product of the length of the secant segment and its external secant segment equals the square of the length of the tangent segment. 𝑃𝐴 2 =𝑃𝐶∙𝑃𝐵

Tangent Line/Segment A line or segment that intersects a circle exactly once.

Dilation A transformation in which the image is similar (but not congruent) to the pre-image.

Reflection A transformation in which a figure is flipped over a line, called a line of reflection.

Rotation A transformation in which each point of the pre-image travels clockwise or counterclockwise around a fixed point a certain number of degrees.

Tessellation A covering of a plane consisting of one or more types of shapes such that there are no overlaps or gaps between the shapes.

Translation A transformation that moves each point of a figure the same distance and in the same direction.

Cone A solid bounded by a circular base and a curved surface with one vertex

Cross Section The intersection of a solid figure and a plane.

Cylinder A solid bounded by two congruent and parallel circular bases joined by a curved surface.

Edges The line segment formed by the intersection of two faces of a polyhedron.

Faces One of the polygons that make up a three dimensional solid figure.

Hemisphere A half-sphere.

Isometric Drawing A drawing on isometric dot paper the represents a three-dimensional figure and shows the top, side, and front views.

Lateral Area The surface area of a solid excluding the base(s).

Lateral Faces The nonparallel bases, or bases, of a solid.

Net A two-dimensional drawing used to represent or form a three-dimensional object or solid.

Oblique Not perpendicular.

Polyhedron A closed three-dimensional figure consisting of polygons that are joined along their edges.

Prism A polyhedron that has two congruent parallel faces (bases) that are joined by faces that are parallelograms.

Pyramid A polyhedron with three or more triangular faces that meet at a point (vertex) and one other polygonal face called the base.

Slant Height It is the shortest distance from the vertex of a cone or pyramid to the edge of the base.

Sphere The set of all points (x, y, z) that are a given distance, the radius, from a point, the center.

Surface Area The total area of all the surfaces of a three-dimensional figure.

Volume The number of cubic units in a three-dimensional figure.