Big Ideas Math Geometry Chapter 1-5 Vocabulary
Corresponding Angles Converse
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Center of Symmetry
Point that a shape rotates around
Point
A location in space that is represented by a dot and has no dimension
Non-rigid Motion
A transformation where the size of the shape changes from the pre-image to the image
Ray
AB is a ray if it consists of the endpoint A and all points on line AB that lie on the same side of A as B.
Terminal point
Ending point of a vector
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Corollary to the Converse of the Base Angles Theorem
If a triangle is equiangular, then it is equilateral.
Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular.
Congruent segments
Line segments that have the same length
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180°.
Transformation
A function that moves or changes a figure in some way to produce a new figure called an image
Line
A line has one dimension It is represented by a line with two arrowheads, but it extends without end
perpendicular bisector
A line that is perpendicular to a segment at its midpoint.
corresponding parts
A pair of sides or angles that have the same relative position in two congruent figures.
Segment bisector
A point, ray, line, line segment, or plane that intersects the segment at its midpoint
Vector
A quantity that has both direction and magnitude, or size, and is represented in the coordinate plane by an arrow drawn from one point to another.
Angle bisector
A ray that divides an angle into two angles that are congruent
Coordinate
A real number that corresponds to a point on a line
Angle
A set of points consisting of two different rays that have the same endpoint
corollary to a theorem
A statement that can be proved easily using the theorem. The Corollary to the Triangle Sum Theorem states that the acute angles of a right triangle are complementary.
Dilation
A transformation in which a figure is enlarged or reduced with respect to a fixed point and a scale factor.
Rotation
A transformation in which a figure is turned about a fixed point
Rigid Motion
A transformation that preserves a shapes lengths and angle measures
Reflection
A transformation that uses a line like a mirror to reflect a figure.
corresponding angles
Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.
interior angles
Angles of a polygon.
exterior angles
Angles that form linear pairs with the interior angles of a polygon.
consecutive interior angles
Angles that lie within a pair of lines and are on the same side of the transversal.
alternate interior angles
Angles that lie within a pair of lines and on opposite sides of a transversal.
Component form of a vector
Combines the horizontal and vertical components of a vector in the form of <H,V> for example <1,2>
Opposite rays
If point C lies on line AB between A and B, then ray CA and ray CB are opposite rays.
Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Converse of the Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Linear Pair Perpendicular Theorem
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Side-Angle-Side (SAS) Congruence Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
Slopes of Parallel Lines
In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
Slopes of Perpendicular Lines
In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is -1. Any horizontal line and vertical line are perpendicular.
skew lines
Lines that do not intersect and are not coplanar.
Coplanar points
Points that lie in the same plane
Collinear
Points that lie on the same line
Endpoints
Points that represent the ends of a line segment or ray
When the scale factor 0 < k < 1
Reduction
Initial point
Starting point of a vector
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary.
vertex angle
The angle formed by the legs of an isosceles triangle.
Vertex of an angle
The common endpoint of the two rays that form an angle
distance from a point to a line
The length of the perpendicular segment from the point to the line.
Line of reflection
The line that a shape reflects across
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles
Image
The new figure after a transformation occurs
Pre-image
The original figure before a transformation occurs
Center of rotation
The point that a figure rotates around during a rotation.
Midpoint
The point that divides a segment into to congruent segments
Scale Factor
The ratio of the lengths of the corresponding sides of the image and the pre-image
Interior of an angle
The region that contains all the points between the sides of an angle
Exterior of an angle
The region that contains all the points outside of an angle
Intersection
The set of points two or more geometric figures have in common
base of an isosceles triangle
The side of an isosceles triangle that is not one of the legs.
hypotenuse
The side opposite the right angle of a right triangle.
legs of a right triangle
The sides adjacent to the right angle of a right triangle.
base angles of an isosceles triangle
The two angles adjacent to the base of an isosceles triangle.
legs of an isosceles triangle
The two congruent sides of an isosceles triangle
Properties of Triangle Congruence
Triangle congruence is reflexive, symmetric, and transitive.
Linear pair
Two adjacent angles whose noncommon sides are opposite rays
Congruent angles
Two angles that have the same measure
Adjacent angle
Two angles that share a common vertex and side, but have no common interior points
Supplementary angles
Two angles whose measures have a sum of 180°
Complementary angles
Two angles whose measures have a sum of 90⁰
parallel planes
Two planes that do not intersect.
Line symmetry
When a figure can be mapped onto itself by a reflection in a line
Similarity Transformation
A dilation or a composition of rigid motions and dilations.
Segment
Consists of two endpoints and all the points between them
parallel lines
Coplanar lines that do not intersect.
your mom
Enlargement
Similar Figures
Figures with the same shape but not necessarily the same size.
Side-Side-Side (SSS) Congruence Theorem
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Theorem
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Sides of an angle
The rays of an angle
Vertical angles
Two angles whose sides form two pairs of opposite rays
Rotational Symmetry
When a figure can be mapped onto itself by a rotation of 180 degrees or less
Transformation Rule
A Function that describes the movement from the pre-image to the inage in the form of (x,y) ---> (x+2, y-3)
Plane
A flat surface made up of points that has two dimensions and extends without end, and is represented by a shape that looks like a floor or a wall
transversal
A line that intersects two coplanar lines at two distinct points.
Translation
A transformation where every point in the pre-image moves the same distance and direction
Acute angle
An angle that has a measure greater than 0⁰ and less than 90⁰
Obtuse angle
An angle that has a measure greater than 90° and less than 180°
Straight angle
An angle that has a measure of 180°
Right angle
An angle that has a measure of 90°
alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
