Geometry Flash Cards v2

An undefined term in geometry, it names a location and has no size

An undefined term in geometry, a straight path that has no thickness and extends forever

An undefined term in geometry, it is a flat surface that has no thickness and extends forever

A part of a line consisting of two endpoints and all points between them

The point at an end of a segment or the starting point of a ray

A part of a line that starts at an endpoint and extends forever in one direction

Points that lie on the same plane

Lines in the same plane that do not intersect

Planes that do not intersect

Points that lie on the same line

A statement about collinear points

A statement that is accepted as true without proof. Also called an axiom

The distance between two points (x1, y1) and (x2, y2) on the coordinate plane is √((x2-x1)^2 + (y2-y1)^2)

The point that divides a segment into two congruent segments

A line, ray, or segment that divides a segment into two congruent segments

The midpoint M of segment AB with endpoints A(x1, y1) and B(x2,y2) is given by m( (x1+x2)/2, (y2+y1)/2 )

Figure formed by two rays with a common endpoint

The common endpoint of the sides of the angle

Two angles in the same plane with a common vertex and a common side, but no common interior points

One of two the rays that form an angle

An angle that measures greater than 0 degrees and less than 90 degrees

An angle that measures 90 degrees

An angle that measures greater than 90 degrees and less than 180 degrees

A 180 degree angle

A common measurement unit for circular arcs

A ray that divides an angle into two congruent angles

A ray that divides an angle into two angles that both have the same measure

A change in the position, size, or shape of a figure on a graph

The original image in a transformation

The image that results from a transformation of a figure known as the preimage

A transformation that does not change the shape or size of a figure. Examples: reflections, translations, and rotations

Transformations that changes the position of the a figure without changing size or shape

Rigid Motions preservers:

Distance

Angle Measure

Betweenness

Collinearity

Parallelism

A statement that is believed to be true

Example:

A sequence begins with the terms 2, 4, 6, 8, 10

A reasonable conjecture is that the next term in the sequence is 12

The process of reasoning that a rule or statement is true because specific cases are true

The process of using logic to draw conclusions

A statement that has been proven

An example that proves that a conjecture or statement is false

A statement that can be written in form “if p, then q,” where p is the hypothesis and q is the conclusion

If x+1=5 (hypothesis), then x=4 (conclusion)

If a=b, then a+c = b+c

If a=b, then a-c = b-c

If a=b, then ac =bc

If a=b, then a/c = b/c

If a=a, then a=a

If a=b, then b=a

If a=b and b=c, then a=c

If a=b, then b can be substituted for a in any expression

Two angles whose measures have a sum of 180 degrees

A pair of adjacent angles whose non-common side is opposite rays

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

Through any two points, there is exactly one line

Through any three noncollinear points, there is exactly one plane containing them

If two points lie in a plane, then the line containing those points lie in the plane

If two lines intersect, then they intersect in exactly one time

If two planes intersect, then they intersect in exactly one line

A quantity that as both magnitude and direction

The starting point of a vector

The endpoint of a vector

Transformation that shifts or slides every point of a figure or graph the same distance in the same direction

Translation Right:

(x,y)→(x+a,y)

Translation Left:

(x,y)→(x-a,y)

Translation Up:

(x,y)→(x,y+a)

Translation Down:

(x,y)→(x,y-a)

Lines that intersect at 90 degree angles

A line perpendicular to a segment at the segment’s midpoint

A transformation across a line, called the line of reflection, such that the line of reflection is perpendicular bisector of each segment joining each point and its image

Reflection across x-axis:

(x,y)→(x,-y)

Reflection across y-axis:

(x,y)→(-x,y)

Reflection across y=x:

(x,y)→(y,x)

Reflection across y=-x:

(x,y)→(-x,-y)

A transformation about a point p, also known as the center of rotation, such that each point and its image are the same distance from p. All angles with vertex p formed by a point and its image are congruent

The point around which the figure is rotated

An angle formed by a rotating ray, called the terminal side, and a stationary reference called the initial side

90 degree rotation counterclockwise:

(x,y)→(-y,x)

180 degree rotation:

(x,y)→(-x,-y)

270 degree rotation counterclockwise:

(x,y)→(y,-x)

360 degree rotation:

(x,y)→(x,y)

In the transformation of a figure such that the image coincides with the preimage, the image and preimage have symmetry

A figure that can be reflected across a line so that the image coincides with the preimage

A line that divides a plane or figure into two congruent reflected halves

A figure that can be rotated about the point by an angle less than 360 degrees so that the image coincides with the preimage has rotational symmetry

The smallest angle through which a figure with rotational symmetry can be rotated to coincide with itself

A pair of non-adjacent angles formed by two intersecting lines

Two angles whose measures have a sum of 90 degrees

If two angles are vertical angles, then the angles are congruent

A line that intersects two coplanar lines at two different points

For two lines intersected by a transversal, a pair of angles that lie on the same side of the transversal and the same side of the two other lines.

For two lines intersected by a transversal, a pair of angles that lie on the same side of the transversal and between the two lines

For two lines intersected by a transversal, a pair of nonadjacent angles that lie on opposite sides of the transversal and between the two other lines

For two lines intersected by a transversal, a pair of nonadjacent angles that lie on opposite sides of the transversal and between the two other lines

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure

If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the measure

The statement formed by exchanging the hypothesis and the conclusion of a conditional statement

Statement: if n+1=3, then n=2

Converse: if n=2, then n+1=3

If two lines are cut by a transversal so that a pair of same side interior angles are supplementary, the lines are parallel

If two lines are cut by a transversal so that any alternate interior angles are congruent, then the lines are parallel

If two lines are cut by a transversal so that any corresponding angles are congruent, then the lines are parallel

If the point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

If a point is equidistant from the endpoints of the segment, then it lies on the perpendicular bisector of a segment

If the figures are congruent, then corresponding sides are congruent and corresponding angles are congruent

A statement that can be written in the form of “p if and only if q”

Example:

A figure is a triangle only if it is a three sided polygon

A statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement

Example:

Statement: n+1=3, then n=2

Contrapositive: n≠2, then n+1≠3

If two angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the triangles are congruent

If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent

If three sides of a triangle is congruent to three sides of another triangle, then the triangles are congruent

If two angles and the non-included side of one triangle is congruent to two angles and the non-included side of another triangle, then the triangles are congruent

The side opposite the right angle in a right triangle

One of the two sides of the right triangle that form the right angle

If a hypotenuse and a leg of a right triangle is congruent to a hypotenuse and a leg of another right triangle, then the triangles are congruent

The angle formed by two sides of a polygon with a common vertex

A line drawn in a figure to aid in a proof

The sum of the angles measures of a triangle is 180 degrees

The sum of the measures of the interior angles of a convex polygon with n sides (n-2)180

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