Geometry Honors(9th grade)

point : -a location-named with capital letters

acute triangle : A triangle that contains only angles that are less than 90 degrees.

auxiliary line : An extra line or segment drawn in a figure to help complete a proof

exterior angle : An angle formed by one side of a polygon and the extension of an adjacent side

Exterior Angle Theorem : The sum of the remote interior angles is equal to the measure of the exterior angle.

Triangle Sum Theorem Corollaries : 1. The acute angles of a right triangle are complementary.2. There can be AT MOST one right or obtuse angle in a triangle.

Properties of Triangle Congruence : Triangle congruence is reflexive, symmetric, and transitive.

included angle : An angle created by two adjacent sides

Angle-Angle-Side (AAS) Congruence Theorem : If 2 angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

legs of an isosceles triangle : the two congruent sides of an isosceles triangle

Equilateral Triangle Corollaries : 1. a triangle is equilateral if an only if it is equiangular 2. each angle in an equilateral triangle measures 60 degrees

coordinate proof : A proof involving placing geometric figures in a coordinate plane.

Circumcenter Theorem : The circumcenter of a triangle is equidistant from the vertices of the triangle

Incenter : the point of concurrency of the angle bisectors of a triangle

Centroid Theorem : The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side

altitude of a triangle : a perpendicular segment from a vertex to the line containing the opposite side

Triangle Inequality Theorem : The sum of any two side lengths of a triangle is greater than the third side length

The Hinge Theorem (SAS Inequality Theorem) : If 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angles are NOT congruent, then the longer third side is opposite the larger included angle.

alternate interior angles : angles between 2 lines and on opposite sides of a transversal

alternate exterior angles : Angles that lie outside a pair of lines and on opposite sides of a transversal.

slope : Rise over run (change in y, for every change in x)

rate of change : A rate that describes how one quantity changes in relation to another

Converse of the Corresponding Angles Postulate : If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.

Parallel Postulate : Through a point P not on line l, there is exactly one line parallel to l.

corresponding angles : Angles in the same place on different lines

parallel lines : coplanar lines that do not intersect

exterior angles : The four outer angles formed by two lines cut by a transversal (NOT BETWEEN the two lines)

Line Postulate : Through any two points there is exactly one line

Intersecting Lines Postulate : If two lines intersect, then they intersect in exactly one point

Intersecting Planes Postulate : If two planes intersect, then their intersection is a line.

Angle Addition Postulate : If P is in the interior of <RST, then m<RSP + m<PST = m<RST

Supplement Theorem : If two angles form a linear pair, then they are supplementary angles

Vertical Angles Theorem : Vertical angles are congruent

Right Angle Theorem : All right angles are congruent

reflection symmetry : A shape with two halves that are mirror images of each other.

line of symmetry : a line that divides a figure into two halves that are mirror images of each other

Dilation : Enlarging or reducing a figure proportionally.

similarity transformation : When a figure and its transformation image are similar (but not necessarily the same size)

dilations in the coordinate plane : (x,y) --> (kx, ky)

undefined term : A basic figure that is not defined in terms of other figures. The undefined terms in geometry are point, line, and plane.

constructions : methods of creating these figures without the benefit of measuring tools

vertex : The common endpoint of an angle

axiom : a statement that is accepted as true without proof

n-gon : a polygon with n sides

reflection : A transformation that "flips" a figure over a mirror or reflection line.

hypothesis : ...

line : -made up of points, -no thickness of width, -needs 2 points to make-goes forever in both directions-cannot be measured

plane : -flat surface-made up of 3 points

opposite rays : -two rays go in opposite directions-form a line-common endpoint

intersection : -common points-shared points

angle : -formed by two noncollinear rays that have a common endpoint

right angle : -measure 90 degrees

adjacent angles : -angles that are next to each other-two angles that lie in the same plane-have common vertex-share common side-no common interior points(doesn't overlap)

vertical angles : -two non-adjacent angles formed by two intersecting lines-always congruent

polygon : -figure in a plane formed by 3 or more segments(sides)

convex : -no line containing a side contains interior points of the polygon

transformation : -change; a mapping for which each point has exactly one image point and each image point has exactly one preimage point

congruent transformation : -a change that maintains shape and size

y-axis reflection : (x,y) -> (-x,y)

180 degree rotation about origin : (x,y) -> (-x,-y)

proof : -used to prove a conjecture true-logical argument in which each statement you make is supported by a statement that is accepted as true.

counterexample : -used to prove a conjecture false-one specific example of when a conjecture fails

negation : -making a statement say the opposite -〰p "not p"

inverse : -negating both the hypothesis and conclusion of the conditional -〰p➡️〰q "if not p, then not q"

Law of Syllogism : -transitive property-if p➡️q is true and q➡️r is true, then p➡️r is also true

postulate : -a statement/ rule that is accepted true (it is a fact and doesn't need to be proven)

subtraction property of equality : -if a=b, then a-c=b-c

multiplication property of equality : -if a=b, then ac=bc

Transitive property of equality : -same as transitive prop of equality except it is for congruence (theorem)

right angle congruence theroem : -all right angles are congruent