# Geometry Exam Trimester 1

This is for the Geometry Exam Trimester 1. Terms not in any order.

## Terms

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Complementary Angles
2 angles whose sum is 90 degrees. Each angle is the other's complement (90-x)
Union (U)
All points that are contained in each figure
2 angles with a common vertex which share a side, but do no have any common interior points.
Contrapositive
The negation of the converse of the conditional [not q → not p]
Triangle
The union of segments joining 3 non-collinear pts
Circle
Is the set of all points in a plane a given distance from a given point. This distance is called the radius. (plural - radii)
CCAC (Compliments of Congruent Angles are Compliments)
If 2 angles are complementary to the same angle or congruent angles, then they are congruent - Complements of congruent angles are congruent.
4 Parts of Reason
1) Given - 2) Definition - 3) Postulate - 4) Previously Proven Theorem
Deductive Reasoning
A system of thought based on statements that have already been proven or accepted by fact
CPCTC
If 2 triangles are congruent, then their parts are congruent
Angle Bisector
A ray that divides an angle into 2 congruent angles
Midpoint Formula
Given a number line, if you need to find the coordinate of the midpoint of the segment joining two point, then average the coordinates of the segment's endpoints.
Circle
A set of all points in a given plane; named by its center point
HL Postulate (Hypotenuse Leg congruent triangles)
If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent.
Ven Diagram hypothesis
Is always the smaller circle
Equilateral Triangle
A triangle with all three sides congruent
Concurrent Lines
Lines that meet at exactly one point
Collinear Points
Points that can be contained on the same line
Subtraction property of equality
If a = b and c = d, then a - c = b - d or if a = b then a - c = b - c.
Linear Pair
2 adjacent angles whose outside ray form a straight line
Legs (Isosceles Triangle)
Refers to the congruent sides of an isosceles triangle
SCAC (Supplements of Congruent Angles are Congruent)
If 2 angles are supplementary to the same angle or congruent angles, then they are congruent - Supplements of congruent angles are congruent.
Equiangular Triangle
A triangle in which all angles are congruent
PBT ( Perpendicular Bisector Theorem)
If a point lies on the perpendicular bisector of a segment then the point is equidistant from the endpoints of the segment.
Scalene Triangle
A triangle with no congruent sides
Perpendicular
If 2 lines, rays, or segments intersect and form right angles, they are perpendicular
Triangle Inequality Theorem [Idea]
Third side is greater than the distance[d] and less than the sum[s]. (d
When reasoning a conditional with a ven diagram..
... If there is only one place to put the 'person' then then a conclusion can be made
Vertical Angles
Formed when the rays forming the sides of one and the rays forming the sides of the other are opposite rays
Altitude of a Triangle
The segment drawn from a vertex, perpendicular to the line containing the opposite side, creating right angles; sometimes referred to as the height of the triangle
Division Property
If segments or angles are congruent, their like divisions are congruent.
SSS (Side Side Side congruent triangles)
If there exists a correspondence between the vertices of two triangles such that the three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.
Assumptions NOT allowed on a given diagram
Congruent angles unless marked, right angles unless marked, size of angles and segments
Right Triangle
A triangle with 1 right angle. The side opposite the right angle is called the hypotenuse. The sides that form the right angle are called legs.
SAT (Straight Angle Theorem)
All straight angles are congruent
Auxiliary Line
An extra line added in a diagram to aid in the solution of a proof
Line segment
A portion of a line containing 2 points and all points between them
Logical Equivalent
When the original conditional is true/false then the contrapositive is must be true/false; also applied to the inverse and converse
Obtuse Angle
An angle whose measure is larger than 90 degrees and less than 180 degrees
Triangle Inequality
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Median of a Triangle
The segment that joins a vertex of a triangle to the midpoint of the opposite side. Every triangle has three
Ven Diagram conclusion
Is always the bigger circle
Median of a Triangle
The segments that join a vertex of a triangle to the midpoint of the opposite side
Ray
A portion of a line beginning at a point and extending infinitely in 1 direction. The endpoint is where the ray begins
LPSUP (Linear Pairs are Supplementary)
Linear pairs are supplementary.
Triangle Inequality Theorem
The sum of the lengths of any two sides must be greater than the length of the third side
Centroid
The point where the medians of a triangle meet inside the triangle; is the center of mass of that triangle
Division property of equality
If a = b and c = d, then a / c = b / d or if a = b then a / c = b / c.
Endpoints
The 2 points that mark the boundaries of the segment
Conditional Statement
A statement that is written in the form of "If __(hypothesis)___, then ___(conclusion)___"; Definitions, postulates, and theorems can be written in this manner
Centroid
The point of concurrency of the medians of a triangle. This is also known as center of mass or center of gravity or point of equilibrium.
Inductive Reasoning
A system based on observation; is not always true
CSAR (Congruent Suppliments Are Right angles)
If two angles are both congruent and supplementary, then they are right angles.
VAT (Vertical Angle Theorem)
All vertical Angles are congruent.
Chain Reasoning
When more than one conditional is given, and the connection between the conclusion of one to the hypothesis of the next is made
Orthocenter
The point of concurrency of the lines containing the altitudes of a triangle
SAT (Straight Angle Theorem)
If 2 angles are straight angels, then they are congruent. (Straight Angle Theorem)
Between-ness
If a point is between two other points it must be on the same line
Subtraction Property (angles)
If 2 pairs of congruent adjacent angles are subtracted from each other, then the resulting angles must be congruent.
Vertex Angle (Isosceles Triangle)
The angle located at the intersection of the congruent sides of an isosceles triangle
ROC (Radii of a circle are Congruent
All radii of a circle are congruent
If a = b and c = d, then a + c = b + d or if a = b then a + c = b + c.
5 Parts of a Proof
1) Diagram - 2) Given Information - 3) Proof - 4) Statement - 5) Reason
Incenter
The point where the angle bisectors of a triangle meet; is the center of a triangle's inscribed circle
Point
A point is a position with no size, thickness, or shape.
CITT (Converse of Isosceles Triangle Theorem)
If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.
RAT (Right Angle Theorem)
If 2 angles are right angles, then they are congruent. (Right Angle Theorem)
Line Postulate
Postulate used to introduce auxiliary lines in a proof's diagram
Concurrent lines
lines that intersect at the same point
Subtraction Property (segments)
If congruent segments are subtracted to congruent segments, the resulting segments are congruent.
Angle
A figure formed by 2 rays with the same endpoint.
Perpendicular Bisector
The line perpendicular to a segment passing through the segment's midpoint; in a triangle they meet at the circumcenter
CPBT (Converse of the Perpendicular Bisector Theorem)
If two points are equidistant from the endpoints of a segment, then the line containing those points is the perpendicular bisector of the segment.
Plane
A plane is a flat surface extending indefinitely.
Circumcenter
Where the perpendicular bisectors of the sides of a triangle meet
Reflexive Property
Anything is congruent to itself (a = a).
Orthocenter
The point where the three altitudes of a triangle meet (when this happens)
Theorem
A statement that must be proven
Converse
A sentence where the hypothesis and the conclusion are switched p → q [p = hypothesis, q = conclusion]
Non-collinear Points
Points that cannot be contained on the same line
ASA (Angle Side Angle congruent triangles)
If there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
Obtuse Triangle
A triangle with 1 obtuse angle
Sides of an angle
Rays that make up the angle
Line
A line is a series of points extending on a straight path infinitely in opposite directions.
Equidistant
The distance is the same between two places
Opposite Rays
2 rays with the same endpoint. extending in opposite directions that make up a straight line
Substitution Property
Replacing a quantity or figure with something it is congruent or equal to
Transitive Property
If angles or segments are congruent to the same angle or to congruent angles, they are congruent to each other. If a = b and b = c, then a = c
BSBA (Bigger side, bigger angle)
In a triangle with unequal angles, the bigger side is opposite the bigger angle.
Segment Bisector
Any line, ray, or segment or plane that intersects a segment only at its midpoint
Segment Trisect
If a segment is divided into 3 equal segments it is said to be trisected
Assumptions on a given diagram
Position of Points (collinear, non-collinear, between-ness), straight lines/ angles
Inverse
The negation of the conditional; They opposite of the hypotenuse and opposite of the conclusion [not p → not q]
Postulate
A statement accepted as true without proof
Acute Triangle
A triangle with 3 angles smaller than 90 degrees
ITT (Isosceles Triangle Theorem)
If 2 sides of a triangle are congruent, then the angles opposite the sides are congruent.
Vertex
Endpoint of the rays of an angle
Betweenness
If a point is between two other points it must lie on the same line.
Acute Angle
An angle whose measure is greater than zero and less then 90 degrees
Intersection (∩)
Point[s] that a figure have in common
Base Angles (Isosceles Triangle)
The angles located at the end points of the base of an isosceles triangle
Midpoint
A point that divides the segment into 2 congruent segments
Distance between two points
The length of the segment joining those two points.
CAR
If 2 adjacent angles are complementary, then the angle formed by their outside rays is a right angle.
Right Angle
An angle whose measure is 90 degrees
Straight Angle
An angle whose measure is 180 degrees
Multiplication Property
If segments or angles are congruent, their multiples are congruent.
The distance between the center of a circle to a point on the circumference
Isosceles Triangle
A triangle with at least 2 congruent sides. Legs are the congruent sides of an isosceles. The base is the other side. Base Angles are the angles located at the endpoints of the base. The vertex is the angle between the two congruent sides.
Multiplication property of equality
If a = b and c = d, then a.c = b.d or if a = b then a.c = b.c.
Altitude of a triangle
The segment drawn from any vertex of the triangle to the opposite side, extending if necessary, and perpendicular to that side
BABS (Bigger angle, bigger side)
In a triangle with unequal sides, the bigger angle is opposite the bigger side.
Supplementary Angles
2 angles whose sum is 180 degrees. Each angle is the other's supplement (180-x)
Counterexample
A statement that can be proved incorrect and why
Distance between a point and a line
The perpendicular to the line.
ARC
If a right angle is formed by 2 adjacent angles then the 2 angles are complementary.
Base (Isosceles Triangle)
The third side of an isosceles triangle
What does CPCTC stand for?
Corresponding Parts of Congruent Triangles are Congruent
SAS (Side Angle Side congruent triangles)
If there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.