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Glossary

Adjacent sides: Two sides of a polygon that intersect at a vertex.

Arc: An unbroken part of a circle.

Central angle of a circle: An angle whose vertex is the center of a circle.

Chord: A segment whose endpoints lie on a circle.

Congruent arcs: Arcs, in the same circle or in congruent circles, that have equal measures.

Complementary angles: Two angles, the sum of whose measures is ninety degrees. [5]

Concept attainment: The process of creating categories by grouping similar objects and ideas…and by finding those attributes that are absolutely essential to the meaning and disregarding those that are not.  The adult’s role in the child’s concept attainment process is to provide an enriched, idea-filled environment so that many examples of many concepts are encountered, and information and feedback regarding the accuracy of the concept definitions are given. [1]  

 Conclusion: In a conditional statement, it follows after “Then”; symbolically, it is the q.

Conditional: A statement that tells if one thing happens, another will follow; written as p®q.

Consecutive angles:
Two angles of a polygon that are consecutive of each other.

Contrapositive: A type of conditional statement; if a conditional is p ® q, then its contrapositive is ~q ® ~p.

Congruent triangles:  Triangles whose vertices can be matched in such a way that the corresponding parts of the triangles are congruent.  Congruent figures have the same shape and size. [5]

Converse: A reversed conditional statement; if a conditional is p ® q, then its converse is q ® p.

Diagonal:
A segment joining two nonconsecutive vertices.

Geometric mean: For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that  .

  • Corollary 1: The length of the altitude of the hypotenuse of a right triangle is the geometric mean of the lengths of the sub-segments of the hypotenuse.
     

  • Corollary 2: The altitude of the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse. [5]

Hypotenuse-Leg Theorem (HL):  If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. [5]

Hypothesis:
In a conditional statement, it follows after “If”; symbolically, it is the p.

Implication:
See conditional

Inscribed angle: An angle whose vertex is on a circle an whose sides are chords of the circle.

Inverse: A type of conditional; if a conditional is p ® q, then its inverse is ~p ® ~q.

Isometric drawing: A drawing of a 3-dimensional object that shows a corner view of the figure. [2]  

Isosceles right triangles: A triangle with a right angle.  The right angle is included between two legs of equal length. [5]

Length of an arc: Along a circle, the distance between the endpoints of an arc.

Major arc: Two points on a circle and all the points of the circle not on the minor arc between the two given points. A major arc measures greater than 180° and is named by three points, its endpoints, and a third point on the major arc.

Measure of an arc: The measure of a minor arc is equal to the measure of the central angle that intercepts it. The measure of a major arc is equal to 360° minus the measure of the corresponding minor arc. The measure of a semicircle is 180°. The measure of a complete circle is 360°.

Minor arc: Two points on a circle and all the points of the circle in the interior of the central angle between the two endpoints. A minor arc measures less than 180° and is named by its two endpoints.

Opposite angles: Two angles of a polygon that are opposite of each other.

Opposite sides: Two sides of a polygon that are opposites of each other.

Parallelogram:
A quadrilateral with both pairs of opposite sides parallel.

Point of tangency: The point where a tangent intersects a circle.

Pythagorean Theorem: In a right triangle, the square of the measure of the hypotenuse equals the sum of the squares of the measures of the two legs. [5]

Quadrilateral:
A polygon with four sides.

Rectangle: A parallelogram with four right angles.

Regular polygon: A polygon that is both equilateral and equiangular. [3]

Regular tessellation: A tessellation in which each shape is a regular polygon and all the shapes are congruent. [4]

Rhombus: A parallelogram with four congruent sides.  

Secant of a circle: A line, ray, or segment that contains a chord.

Sector of a circle: A region of a circle that is bounded by two radii and an arc of the circle.

Semicircle:
Either of the two arcs of a circle intersected by a diameter of the circle. A semicircle is named by three points, its endpoints and a third point on the semicircle.

Similarity Ratio:  The ratio of the lengths of corresponding sides of a triangle. [5]

Square: A parallelogram with four right angles and four congruent sides.

Supplementary Angles: Two angles, the sum of whose measure is one hundred and eighty degrees. [5]

 Syllogism:
1. a deductive scheme of a formal argument consisting of a major and a minor premise and a conclusion (as 'every virtue is laudable; kindness is a virtue; therefore, kindness is laudable')
2. a subtle, specious, or crafty argument
3. deductive reasoning.

Tangent to a circle: A line in the plane of the circle that intersects the circle in only one point.

Trapezoid: A quadrilateral with exactly one pair of parallel sides.

Tessellation: A tessellation, or tiling, is a repeating pattern of figures that completely covers a plane without gaps or overlap. [2]  

Transversal: A line (or segment) that intersects two coplanar lines (or segments) at two distinct points. [5]

Venn Diagram:
A diagram that uses circles to represent sets and their relationship.

Vertical Angles: Two nonadjacent angles formed by two intersecting lines. [5]

 


[1] Gunter, Mary Alice, et al. (1999).  Instruction:  A Models Approach.  Massachusetts: Allyn & Bacon. 

[2] Bass, Laurie E., et al.  (1998). Geometry: Tools for a Changing World.  New Jersey:  Prentice-Hall, Inc.

[3] Cord Geometry:  Mathematics in Context.  (1999). Ohio: South-Western Educational Publishing.

[4] Cord Geometry:  Mathematics in Context.  (1999). Ohio: South-Western Educational Publishing.

[5] Sobel, M.A., Maletsky, E.M., Golden, N., Lerner, N., & Choen, L.S. (1990). Geometry. Missions Hills, CA: Glencoe Publishing Company.

[6] Cord Geometry: Mathematics in Context. (1999). New York:  South Western Educational Publishing.

[7] Random House Webster’s College Dictionary. (1997). New York:  Random House, Inc.