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A quadrilateral with two pairs of equal, adjacent (touching) sides.

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When two or more parts are identical after a flip, slide or turn. The simplest type of Symmetry is "Reflection" (or "Mirror") Symmetry.

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All rigid motions map lines to lines, segments to segments, and rays to rays. All rigid motions preserve distance and angle measurements. Rotation of a line 180 degrees about a point not on a line produces a parallel line. Rotation of a line 180 degrees about a point on a line produces the same line. Translation of a line not along the line produces a parallel line. When a point is reflected across a line, the segment connecting the point and its image is perpendicularly bisected by the line.

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The same shape and size, but we are allowed to flip, slide or turn. In this example the shapes are congruent (you only need to flip one over and move it a little). Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length.

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either of the angles of a triangle that have one side in common with the base.

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When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

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any transformation, as a translation or rotation, of a set such that the distance between points is preserved.

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Composition of Rigid Motions (translation, rotation, and reflection)

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The distance from the center to any point on the shape stays the same.

Every point makes a circle around the center:

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A flat shape with 4 straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal. It is a type of parallelogram.

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Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Two lines or shapes that lie exactly on top of each other.

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A flat shape with 4 straight sides where opposite sides are parallel.

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A triangle with two equal sides. The angles opposite the equal sides are also equal.

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A line that cuts across two or more (usually parallel) lines.

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A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

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Every point is the same distance from the central line. The reflection has the same size  and shape as the original image

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A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").

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A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.

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Geometry Proofs - Two Column Proofs - MathHelp.com

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For a complete lesson on geometry proofs, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to set up and complete two-column Geometry proofs using the properties of equality as well as postulates and definitions from Geometry.

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To be congruent means to be the same size and shape. Two triangles are congruent if their corresponding angles and sides are congruent.

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Triangle Congruence Statement - How to Write (Geometry)

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The point about which an angle is measured is called the angle's vertex, and the angle  associated with a given vertex is called the vertex angle.

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When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.

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A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

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"Sliding": moving a shape without rotating or flipping it. The shape still looks exactly the same, just in a different place.

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Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

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The line or line segment that divides the angle into two equal parts. The angle bisectors meet at the in center.

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

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A portion of the circumference of a circle.

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The center of a circle is the point equidistant from the points on the edge.

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A circle is all points in the same plane that lie at an equal distance from a center point. The circle is only composed of the points on the border. ... A circle is the same as 360°.

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Two angles are called complementary when their measures add to 90 degrees.

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Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees.

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Reflex angles are angles measuring greater than 180 degrees and less than 360 degrees.

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An angle of 180°.

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Acute angles measure less than 90 degrees.

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An angle of 90°, as in a corner of a square or at the intersection of two perpendicular straight lines.

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An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.

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Parallel lines are lines in a plane which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel.

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Any geometric figure that can pass through (or sit on) the line segment can form a segment bisector. A segment bisector is a geometric figure that divides the line segment exactly in half.

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SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent. ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

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A set A is a subset of another set B if all elements of the set A are elements of the set B. In other words, the set A is contained inside the set B. ... Since B contains elements not in A, we can say that A is a proper subset of B

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What Does Subsets Mean in Math? : Math for Everyone

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A straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter.

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Geometry: Introduction to Circles - radius, diameter, circumference and area of a circle

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Small, shortage, having a lesser amount of something; sharp, quick.

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Acute definition and meaning | Collins English Dictionary

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Acute definition: You can use acute to indicate that an undesirable situation or feeling is very severe or... | Meaning, pronunciation, translations and examples

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Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

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The other ray of an angle, that is not fixed along the positive x-axis, which is called the terminal side of an angle.

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One side of the angle is always fixed along the positive x-axis. This is called the initial side of the angle.

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Each angular point of a polygon, polyhedron, or other figure.

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The measure of the angle formed by the two rays or arms at a common vertex. Angles are measured in degrees with a protractor.

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The figure formed by two rays meeting at a common end point.

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A line of points that extends infinitely in two directions.

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A flat surface that is infinitely large and with zero thickness

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A point on a line segment that divides it into two equal parts. The halfway point of a line segment

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The same shape and size, but we are allowed to flip, slide or turn.

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A triangle with all three sides of equal length.

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A center is a point that is the same distance from all the extremities of a figure.

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Lines that are at right angles (90°) to each other.

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The part of a line that connects two points.

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A part of a line with a start point but no end point (it goes to infinity).

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Three or more points that fall on a straight line.

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Postulate is a true statement, which does not require to be proved. Is used to derive the other logical statements to solve a problem.

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Angle Addition Postulate - MathHelp.com - Geometry Help

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For a complete lesson on angle addition postulate and angle bisector, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the angle addition postulate and the definition of an angle bisector. Students also learn the definitions of congruent angles and adjacent angles.

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Axiom is a rule or a statement that is accepted as true without proof. An axiom is also called a postulate.

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Distance is a numerical measurement of how far apart objects or points are.

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A precise location or place on a plane. Usually represented by a dot.