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Geometry Exam Review - Definitions

Terms

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Circumcenter
The point of intersection of the three perpendicular bisectors in a triangle
Corresponding Angles
Two angles that occupy corresponding positions on a transversal
CPCTC
Corresponding parts of congruent triangles are congruent
Regular Polygon
A polygon with all sides and all angles equal
Parallelogram
A quadrilateral whose opposite sides are both parallel and congruent
Converse
The converse of a conditional statement is formed by interchanging the hypothesis and conclusion
Hypothesis
An educated guess
Acute Angle
An angle that is less than 90°
Interior of an Angle
A point that is between points that lie on each side of the angle
Conditional Statement
A statement which has the form "If P, then Q", which can be written as p>q
Equiangular Polygon
A polygon in which all of its angles are congruent to each other
Perpendicular Bisector
A line or segment passing through the mid pt. of one of the sides perpendicular to that side
Concurrent
Two or more lines or segments that intersect at a single point
Altitude
A segment from a vertex that is perpendicular to the opposite side
Ray
A straight line extending from a point
Subtraction Property of Equality
If a = b then a - c = b - c
Rhombus
A parallelogram with four equal sides
Alternate Exterior Angles
Two angles opposite each other that lie outside two parallel lines cut by a transversal
Angle
Consists of two different rays that have the same initial point
Line Segment
A part of a line
Perpendicular
Two lines that intersect to form right angles
Substitution Property of Equality
If a=b, then b can be substituted for a in any equation
Consecutive Interior Angles
Two angles that lie between two parallel lines on the same side of the transversal
Transitive Property of Equality
If a=b and b=c, then a=c
Conclusion
Represented by Q in conditional statements
Base of a Trapezoid
One of 2 parallel sides of the trapezoid
Counterexample
An example of a conditional statement in which the hypothesis is fulfilled and the conclusion is not fulfilled proves that the statement is false
Obtuse Triangle
A triangle that contains an obtuse interior angle
Parallel Lines
Two lines on the same plane that will never intersect each other
Contrapositive
The contrapositive of a conditional statement is true if and only if the conditional statement is true
Centroid
The point of intersection of the three medians in a triangle
Midpoint
The point that divides a line segment in half
Incenter
The intersection point of a triangle's three angle bisectors
Equiangular triangle
A triangle in which all of its angles are congruent to each other
Segment Bisector
A line, segment, or ray that goes through a midpoint of a segment
Right Angle
An angle whose measure is equal to 90°
Concave Polygon
A polygon in which if any line is extended in it, no point will ever lie in the interior of the polygon
Legs of a Trapezoid
The nonparallel sides of a trapezoid
Complementary Angles
A pair of angles whose measurements add up to 90°
Vertical Angles
Angles are formed opposite of each other when two lines intersect
Supplementary Angles
Two angles that add to 180º
Alternate Interior Angles
Two angles opposite each other that lie between two parallel lines cut by a transversal
Kite
A quadrilateral that has two pairs of consecutive congruent sides but opposite sides are not congruent
Isosceles Trapezoid
A trapezoid whose legs are congruent
Isosceles Triangle
A triangle with two congruent sides
Opposite Rays
Two rays with the same initial point that go in opposite directions
Median
A line passing through the mid pt. of a side and through the opposite vertex
Obtuse Angle
An angle between 90º and 180º
Polygon
A shape with straight sides that is simple and closed
Paragraph Proof
A proof in the format of a paragraph
Right Triangle
A triangle with one right angle
Base Angles of a Trapezoid
One pair of consecutive angles whose common side is a base of a trapezoid
Symmetric Property of Equality
If a=b, then b=a
Linear Pair
Two adjacent angles whose non-common sides are opposite rays
Oblique
Lines that intersect but are not perpendicular
Reflexive Property of Congruence
Any figure is congruent to itself
Exterior of an Angle
Any point that is not on the angle or inside the interior of the angle is on the exterior angle
Congruent
States that two or more shapes or segments are equal in measure
Hypotenuse
The side of a right triangle opposite the right angle
Acute Triangle
A triangle whose interior angles are all acute
Midsegment of a Trapezoid
A segment whose endpoints are the midpoints of the non-parallel sides of the trapezoid
Equilateral Polygon
A polygon in which all of its sides are congruent to each other
Convex
Non-concave
Scalene Triangle
A triangle with no congruent sides
Midsegment of a Triangle
A line segment that connects the midpoints of two sides of a triangle
Adjacent Angles
2 angles that share a side and vertex but no interior points
Transitive Property of Congruence
If a≅b and b≅c, then a≅c
Trapezoid
A quadrilateral with one pair of parallel sides
Addition Property of Equality
It states that if you add the same value to each side of an equation, the results are equal. (If A = B, then A + C = B +C)
Square
Having four equal sides and every angle a right angle
Exterior Angle
The outside of an angle
Rectangle
A parallelogram with four right angles
Multiplication Property of Equality
Multiplying the same quantity to both sides of an equation. (If a=b, then ac=bc)
Orthocenter
The intersection point of a triangle's three altitudes
Diagonal
The segment that joins two nonconsecutive vertices
Slope-Intercept Equation
Y=m(x)+b
Included Angle
The angle that is created where two adjacent angles meet
Reflexive Property of Equality
When something equals itself
Division Property of Equality
Dividing the same quantity to both sides of an equation. (If a=b, then a/c=b/c)
Line
Something straight that holds an infinite amount of points and never ends
Angle Bisector
A segment that bisects one of the angles of the triangle
Skew
Lines that never intersect but are not parallel
Straight Angle
An angle of 180º
Equilateral Triangle
A triangle in which all of its sides are congruent to each other

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