**Acute Angle -** An angle who's measure is less than 90 degrees.

**Acute Triangle** - A triangle with three acute angles.

**Adjacent Angles -** Two angles that share a common vertex, side, or ray.

**Altitude of a Triangle-** A perpendicular segment from a vertex that extends to the opposite side.

**Angle of Depression-** When you look *down* at an object, the angle your line of sight makes with a line drawn horizontally.

**Angle of Elevation-** When you look *up* at an object, the angle your line of sight makes with a line drawn horizontally.

**Alternate exterior angles -** Two angles that are formed by two lines and a transversal and lie outside the two lines and on opposite sides of the transversal.

**Alternate interior angles** - Two angles that are formed by two lines and a transversal and lie between two lines and on opposite sides of the transversal.

**Angle -** Two different rays with the same endpoint.

**Angle Bisector -** A ray that cuts in half an angle into two angles that are congruent.

**Area -** The amount of surface covered by a figure.

**Axiom-** A rule accepted without proof, also called a postulate.

**Bases of a trapezoid -** the parallel sides of a trapezoid.

**Base Angles of a trapezoid**- pair of angles whose common side is a base of a trapezoid

**Biconditional Statement-** A statement that contains "if and only if".

**Center of Dilation-** In a dilation, it is a fixed point that a figure is enlarged or reduced with respect to it.

**Centroid**- The point of concurrency when it is inside the triangle.

**Circle -**

**Circumcenter of a triangle-** The point of concurry of the three perpendicular bisectors of the triangle.

**Circumference -** The distance around a circle.

**Collinear Points -** Points that are on the same line.

**Complementary Angle** - Two angles whose measures have the sum 90 degrees.

**Concave Polygon-** A polygon that is not convex.

**Concurrent-** Three or more lines,rays, or segments that intersect at the same point.

**Conditional Statement-** A type of logical statement that has two parts, a hypothesis and a conclusion.

**Congruent Angles -** Angles that have the same measure.

**Congruent Segments -** Line segments that have the same length.

**Conjecture**- An unproven statement based on observations.

**Consecutive Interior Angles** - Angles that lie between two lines and are on the same side of the transversal.

**Constant -** The number that you start out with in a problem. It doesn't change.

**Converse** - The statement formed by exchanging the hypothesis and conclusion of a conditional statement.

**Convex Polygon- **A polygon if no line contains a side.

**Coordinate-** The real number that corresponds to a point on a line.

**Coordinate Proof-** involves placing geometric figures in a coordinate plane.

**Coplanar Points -** Points that are on the same plane.

**Corollary to a Theorem-** is a statement that can be proved easily using the **Corollary to the Triangle Sum Theorem**.

**Cosine**- A trigonometric ratio, abbreviated *cos*. For a right triangle ABC, the cosine of the acute <A is:

**Counterexample**- A specific case for which the conjecture is false

**Deductive Reasoning -** An argument that can be formed using facts, definitions, accepted properties and the laws of logic

**Defined term** - Described as a point, line, segments, rays, etc.

**Diagonal -** **a segment within a polygon that joins two**** ****vertices that do not folllow each other.**

**Diameter -** the distance from one point of the circle to the other in which it bisects the circle.

**Dilation -** A transformation that stretches or shrinks a figure to create a similar figure. A dilation is a type of similarity transformation.

**Distance -** The absolute value of the difference between two coordinates.

**Distance from a point to a line-** The length of the perpendicular segment from the point to the line.

**Endpoints - **Two points on the end of the line, where all points on that line lie in between the endpoints.

**Equiangular -** All angles in the interior of the polygon are congruent.

**Equidistant-** The same distants from one figure as from another figure.

**Equilateral Polygon - **All sides of a polygon are congruent.

**Equilateral Triangle** - triangle with three congruent sides.

**Equivalent Statements -** In general, when two statements are both true or both false, they are called equivalent statements.

**Exterior Angles-** angles that form linear pairs with the interior angles. It is the angle that is outside of the polygon.

**Extremes-** *a* and *d* in the proportion

**Geometric Mean-** for two positive numbers a and b, the positive number x that satisfies . So, and

**Heptagon -** A seven sided polygon

**Hexagon -** A six sided polygon

**Hypotenuse-** The side that is opposite of the right angle in a right triangle.

**Hypothesis -** The "if" part of a conditional statement

**Incenter****-** The point of concurrency of the three angle bisectors of a triangle

**Included Angle-** The angle that is in between the two given lines or rays.

**Indirect Proof-** A proof in which you prove a statement is false by already assuming it's opposite is true

###

**Inductive Reasoning -** When you find a pattern in specific cases and then write a conjecture for the general case

**Initial Condition -** The number(s) that you start out with. They don't change.

**Interior Angles-** the original angles of the polygon.

**Intersection** - Where two lines or planes meet

**Inverse** - The statement formed by negating the hypothesis and conclusion of a conditional statement.

**Inverse Tangent** - If tan A = x, then tan-1 x = measure of angle A.

**Inverse Sine -** If sin A = y, then sin-1 x = measure of angle A.

**Inverse Cosine -** If cos A = z, then cos-1 x = measure of angle A.

**Isosceles Trapezoid**- A trapezoid with congruent legs.

**Is****osceles Triangle**- triangle with at least two congruent sides.

**Kite-** A quadrilateral that has 4 consecutive congruent sides, but the opposite sides arn't congruent.

**Legs of a Right Triangle-** The sides *adjacent* to the right angle.

**Legs of a Trapezoid-** the nonparallel sides of a trapezoid.

**Line -** Extends infinitely. Any two points create a line.

**Line Segment -**Consists of a line with two endpoints.

**Linear Pair -** Two adjacent angles whose noncommon sides are opposite rays.

**Line Perpendicular to plane-** is a line that intersects the plane in a point and forms a 90 degree angle at the exact point including the rest of the intersections.

**Midpoint -** A point that divides the segment into two congruent segments.

**Midsegment of a Trapezoid-** A segment that connects the midpoints of the legs of a trapezoid.

**Midsegment of a triangle-** is a segment that connects the midpoints of two sides of the triangle.

**Means-** *b* and *c* in the proportion

**Negation**- the opposite of the original statement.

**n-gon - **It is where *n* is the number of a polygon's sides.

**Obtuse Angle -** An angle whose measure is greater than 90 degrees.

**Obtuse Triangle** - triangle with one obtuse angle.

**Octagon** - A polygon with eight sides.

**Opposite Rays -** Two rays that share a common end point and point in different directions.

**Orthographic projection****-** a two-dimensional drawing representing an object formed by the perpendicular intersections of lines

**Paragraph Proof-** A proof written in the form of a paragraph.

**Parallelogram- A quadrilateral with both pairs of opposite sides parallel and congruent. Its opposite angles are also congruent.**

**Parallel li**nes- Two lines in a plane that will continue forever and never intersect.

**Parallel planes-** Two planes that will never intersect.

**Perimeter -** The distance around a figure.

**Perpendicular Bisector-** A segment, line, or ray that is perpendicular to a segment at its midpoint.

**Perpendicular Lines** - Two lines that intersect to form a right angle.

**Plane** - Has two dimensions. Any three points that are not on the same line is a plane.

**Point -** Cannot be measured in any dimension, Thus that has no part. It is a dot that is like a period.

**Point of Concurrency-** The point of intersection of the concurrent lines,segments, or rays.

**Polygon -** A closed-plane figure that has 3 or more sides that do not curve.

**Postulate-** A rule accepted without proof.

**Proof-** A logical argument to show a statement is true.

**Proportion-** An equation that states that two ratios are equal where a and d are the extremes and b and c are the means.

**Pythagorean Triple**- A set of three positive integers *a, b,* and *c* that satisfy the equation .

**Quadrilateral -** A four sided polygon

**Ratio -** A comparison of two numbers using division. The ratio of a to b, where b cannot equal 0, can be written as a to b, a : b, or as

**Rate of Change -** The number that is multiplied by the variable.

**Ray -** A line that has a beginning but no end.

**Rectangle**- A parallelogram with 4 right __angles.__

**Regular -** A polygon is considered regular if it is equiangular and equilateral.

**Rhombus-** A parallelogram with 4 __congruent sides.__

**Right Angle - **An angle who's measure is equal to 90 degrees.

**Right Triangle** - triangle with one right triangle.

**Same-Side Interior Angles** - Another name fo consecutive interior angles.

**Scale Drawing -** 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.

**Scale Factor** - The ration of the lengths of two corresponding sides of two similar polygons

**Scale Factor of Dilation** -The ratio of a side length of he image of the corresponding side length of the original figure.

**Scalene Triangle** - triangle with no congruent sides.

**Segment Bisector -** A point, ray, line, line segment, or a plane that intersects the segment at its midpoint.

**Sides** - The rays of an angle.

**Similar polygons** - Two polygons that have corresponding angles that are congruent and corresponding side lengths that are proportional

**Sine**- A trigonometric ratio abbreviated as *sin*. For the right triangle ABC, the sine of the acute angle A is:

**Skew lines-** Lines in different planes that will never intersect.

**Slope** - The ratio of vertical change (rise) to horizontal change (run) between any two points of a nonvertical line.

**Slope Intercept Form** - The general form of a linear equation, example: y = *m*x + *b*, where *m* is the slope and *b* is the y intercept.

**Solve a Right Triangle-** When solving a right triangle that means you need to find the measure of all the sides and angles.

__2 methods__ used to solve right triangles:

- Two side lengths

- One side length and the measure of one acute angle

**Square**- A parallelogram with 4 __right angles__ & 4 __congruent sides.__

**Standard Form** - An equation written as Ax + By = C, where A and B are not both zero.

**Straight Angle** - An angle whose measure is 180 degrees.

**Supplementary Angles -** Two angles whose measures have a sum of 180 degrees.

**Tangent**- A trigonometric ratio, abbreviated as *tan*. For a right triangle ABC, the tangent of the acute angle A is:

**Theorem-** A statement which can be proven.

**Transversal-** A line that intersects more than one line.

**Trapezoid-** A quadrilateral with one pair of parallel sides called *bases* and two nonparallel sides called *legs.*

**Transitional Words** - Words such as so, then, and therefore, that are used in paragraph proofs to help to make the logic clear.

**Triangle** - A three sided polygon

**Trigonometric Ratio**- A ratio of the lengths of two sides in a right triangle.

**Two-Column Proof -** Numbered statements and corresponding reasons that show an argument in logical order

types of slope- Positive slope (rising line), negative slope (falling line), zero slope (horizontal line), and undefined slope (vertical line).

**Vertex -** The endpoint of an angle.

**Vertical Angles -** Two angles that their sides form two pairs of opposite rays.

**Volume of a solid** - The number of cubic units contained in theinterior of a solid.

**X - intercept -** is the x - coordinate of a point where a graph crosses the x - axis.

**Y - intercept** - is the y - coordinate of a point where a graph crosses the y - axis.

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