Download Geometry Terms

Geometry Terms
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Acute Angle: Less than 90 degrees
Obtuse Angle: Greater than 90 degrees
Length: the absolute value of the distance of two points
Distance: the measure between two points
Absolute Value: The distance from zero
Midpoint: the halfway point of a line segment,
Bisector: divides a segment or angle into two equal halves (or two congruent halves)
Angle: Figure formed by two rays that share a common point (the vertex)
Vertex: common point where the directions change
Interior Angle: an angle formed by two sides of a polygon that share an endpoint
Exterior Angle: The angle between any side of a polygon and an extended adjacent side
Angle Bisector: the line or line segment that divides the angle into two equal halves, congruent pieces
Congruent: same measure, equal
Ray: A line that goes off in one direction forever
Line: A line that goes forever in both directions
Line Segment: A line with two end points or stopping points.
Perpendicular: Intersection creates 90 degree angles (right angle). These lines will have opposite
reciprocals
Parallel: Same slope, lines that never cross
Parallel Angle: Angles formed by parallel lines with congruent interior angles
Vertical Angle: angles are formed from two intersecting lines and the angles are not end-to-end. The
two angles share a vertex and create two sets of congruent angles.
Collinear: A set of points on a line together
Coplanar: A set of points, lines, line segments, rays or any other geometrical shapes that lie on the
same plane
Complimentary Angles: Two angles that added together equal 90 degrees
Supplementary Angles: Two angles that added together equal 180 degrees
Conditional Statement: If, then statement ex. “If You Study Then You’ll Pass”
Negation/Inverse: A “No” statement or the opposite of Conditional ex. “IF You Don’t Study Then You
Won’t Pass”
Converse: Switches order of the Hypothesis and Conclusions “If You Pass Then You Studied”
Contrapositive: Flips the order and negates them.
Inductive Reasoning: Patterns or observations
Deductive Reasoning: Facts or rules
Biconditional Statement: The conditional and the converse must be true. Put the “if” in the middle of
the hypothesis and the conclusion. You can write a biconditional state if the conditional and the
converse are true.
Law of Syllogism: If p→q and q→r are true statements, then p→r is a true statement
o Three Statements: Conditional, then the conclusion implies another truth, if so then the
hypothesis implies the same truth.
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Law of Detachment: If p→q is a true statement and p is true, then q is true.
o Three statements- the conditional statement, prove the hypothesis is true, then you know the
conclusion is true.
Transversal: A line that passes through two parallel lines.
Corresponding Angles: A pair of angles created by a transversal that relate or match. Congruent
Linear Pair: Angles that share a vertex and are on the same side of a line. They’re Supplementary
Angles (add up to 180 degrees)
Vertical Angles: Angles that share a vertex and are on opposite sides of the same line. Congruent!
(Have the same measure)
Same Side Interior: Angles on the same side of the transversal and inside. Supplementary
Same Side Exterior: Angles on the same side of the transversal and outside Supplementary
Alternate Interior Angles: Angles on opposite sides of the transversal and inside the lines. Congruent
Alternate Exterior Angles: Angles on opposite sides of the transversal and outside the lines. Congruent
Rigid Transformation/ Isometry: A transformation that does not change shape/size
o Reflection: The shape flips (reflects) across the x-axis or y-axis
o Rotation: The shape rotates 90’ to the right or 90’ to the left or 180’ (driving a car)
o Translation: Shift of up or down/left or right (think 1980s video game)
Scale Factor: The ratio of change/difference between two or more shapes
Dilation: The shape changes in size of the shape (larger or smaller) by a scale factor
Congruent Triangles: REMEMBER ORDER MATTERS!!!
o Side-Side-Side (SSS): Three sides are congruent which means the triangles are congruent
o Side-Angle-Side (SAS): A pair of corresponding sides and the included angle are equal, which
means the triangles are congruent
o Angle-Side-Angle (ASA): A pair of corresponding angles and the included side are equal which
means the triangles are congruent
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o Angle-Angle-Side (AAS): A pair of corresponding angles and a non-included side are equal,
which means the triangles are congruent
o Hypotenuse Side of a Right Angle (HL): Two right triangles are congruent if the hypotenuse and
one leg are equal.
Acute Triangle: A triangle where all angles are less than 90 degrees
Right Triangle: A triangle where one angle is equal to 90 degrees
Obtuse Triangle: A triangle where one angle is greater than to 90 degrees
Median of a Triangle: A segment whose endpoints are a vertex of a triangle and the midpoint of the
opposite side.
o Centroid: The point of a triangle where the three medians of a triangle meet (or are
concurrent). *Centroid is always inside the triangle.
Altitude of a Triangle: Is the perpendicular segment from a vertex to the opposite side or to the line
that contains the opposite side. An altitude can lie inside, on, or outside the triangle.
o Orthocenter: The point where the three altitudes of a triangle meet (or concur). *Does not
have to be inside the triangle*.
Perpendicular Bisector of a Triangle: A line (ray or segment) that is perpendicular to a side of the
triangle at the midpoint of the side. *Does not have to be inside the triangle.
o Circumcenter: The point where three perpendicular bisectors or a triangle concur (or meet).
Angle Bisector of a Triangle: A bisector of an angle of the triangle.
o Incenter: The point in a triangle where three angle bisectors of a triangle concur (or meet).
Concurrent: 3 or more lines, segments or rays that meet at the common point.
Midsegment: A line that connects two midpoints.
We get MORE Specific as we go down the list
Polygon
Triangle------Quadrilateral------Pentagon
Parallelogram
Rhombus--------Rectangle
Square
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Circle: A set of all points that are equal distance from the center of the circle
Chord: A segment with endpoints ON the circle
Diameter: The distance across the circle through the center
Radius: the distance from the center point of the circle to the edge. Half the diameter
Secant: A line that intersects the circle at two point
Tangent: A line that intersects a circle at exactly one point.
o Point of Tangency: Where the tangent intersects the circle and forms a 90 degree angle
Minor Arc: Arc that is less than 180 degrees (needs two letters to name it)
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Major Arc: Arc that is more than 180 degrees. (needs three letters to name it)
Semicircle: Arc that is half the circle. Exactly 180 degrees, formed by a diameter
Central Angle: Angle with a vertex INSIDE the circle
Inscribed Angle: Angles with a vertex ON the circle
Concentric Circles: Circles with a common center
Tangent Circles: Circles that intersect at a single point.
Circle Rules:
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Central Angle = Interior Arc
Inscribed Angle = ½ Interior Arc
2 Exterior Tangents
Radius & Tangent are Perpendicular
Inscribed Angles that share the same arc are Congruent
Opposite Angles of Inscribed quadrilateral are supplementary (equal 180)
If a Radius/Diameter are Perpendicular to a Chord then it bisects the Chord and Arc.
ANGLES
o Central: angle is congruent to arc
o Inscribed: Angle is ½ interior arc
o Inside: (Arc1 + Arc2) /2 = Angle
o Outside: (Big Arc - Small Arc)/2 = Angle
LENGTH MEASUREMENTS:
o 2 Chords: Part * Part = Part * Part
o 2 Secants: Outside (Whole) = Outside (Whole)
o Secant & Tangent: Outside(Whole) = Tan2