Congruence Geometry Final Studying Vocabulary and Theorems

Angle bisector

a line that divides an angle into two congruent angles

Congruent

figures are congruent when they stack perfectly using a sequence of transformations, such as translations, rotations, and reflections

conjecture

a claim that we are trying to either prove or disprove

Converse

a statement that reverses the order of a conjecture

Corresponding

to correspond is to match. When the parts of two figures stack perfectly, the parts are corresponding; ANGLES CAN BE CORRESPONDING AND YET NOT CONGRUENT BECAUSE CORRESPONDING IS BASED OFF OF POSITIONING

Corresponding angles

two angles in the same position and on the same side of a transversal crossed by two lines. When the lines are parallel, the corresponding angles are congruent. Otherwise, they ARE NOT CONGRUENT.

Diagonal

a line segment that connects two non-adjacent vertices of a polygon

equidistant

at equal distances from a given reference point

kite (definition)

a quadrilateral with two pairs of adjacent congruent sides

parallelogram (definition)

a quadrilateral with opposite sides that are parallel

perpendicular bisector

a line that is made of a set of points equidistant from two endpoints of a line segment

prove

to use mathematical reasoning to convince a community that a conjecture is always true

quadrilateral

a polygon with exactly four sides

rectangle (definition)

a quadrilateral with four congruent angles

reflection

a type of rigid transformation that moves every point on a figure to a point directly on the opposite side of the line

rhombus (definition)

a quadrilateral with four congruent sides

rigid transformation

a move that does not change any measurements of a figure

translations, reflections, or rotations

rotation

a type of rigid transformation that does not change any measurements of a figure

square (definition)

a quadrilateral with four congruent angles and sides

straight angle

an angle that measures 180 degrees

translation

a type of rigid transformation the slides every point on a figure along a vector

vertical angles

pairs of angles that are constructed by rotating one angle 180 degrees around its vertex

complementary angles

angles that sum up to 90 degrees

supplementary angles

angles that sum up to 180 degrees

vertical angles

pairs of angles that are constructed by rotating one angle 180 degrees around

linear pair

supplementary angles that have adjacent angles (a pair)

transversal

a line intersecting two other lines

Triangle sum theorem

the interior angles of a triangle sum to 180 degrees

composition

two or more different transformations combined

CPCTC

corresponding parts of conguent triangles and congruent

SSS congruence

three pairs of congruent sides

SAS congruence

two pairs of sides and a pair of angles between the sides

ASA congruence

two pairs of angles and a pair of sides between the angles

AAS congruence

two pairs of angles and a pair of sides not between the two angles

Reflexive property

something is equal to itself

Hypotenuse leg theorem (HL)

the ONLY time SSA works is when you are given a hypotenuse and a leg of a RIGHT triangle

Base angle theorem

an isosceles triangle has congruent base angles

Isosceles triangle

a triangle with two congruent sides

Parallelogram Opposite Sides Theorem

A parallelogram has two pairs of opposite, congruent sides (converse works too)

Parallelogram opposite Angles theorem

a parallelogram has two pairs of opposite, congruent angles (converse works too)

parallelogram adjacent (or consecutive) angles theorem

a parallelogram’s adjacent angles are supplementary (converse doesn’t work)

right angle congruency theorem

all right angles are congruent

Parallelogram (properties; opp sides, opp angles, 2 consecutive angles supplementary, diagonals perpendicular, diagonals congruent, diagonals bisect)

opposite sides are congruent, opposite angles are congruent, 2 consecutive angles are supplementary, diagonals are not always perpendicular, diagonals are not always congruent, diagonals bisect each other

Rectangle (properties; opp sides, opp angles, 2 consecutive angles supplementary, diagonals perpendicular, diagonals congruent, diagonals bisect)

opposite sides are congruent, opposite angles are congruent, 2 consecutive angles are supplementary, diagonals are not always perpendicular, diagonals are always congruent, and diagonals always bisect each other

Rhombus (properties; opp sides, opp angles, 2 consecutive angles supplementary, diagonals perpendicular, diagonals congruent, diagonals bisect)

opposite sides are congruent, opposite angles are congruent, 2 consecutive angles are supplementary, diagonals are always perpendicular, diagonals are not always congruent, diagonals always bisect each other

Square (properties; opp sides, opp angles, 2 consecutive angles supplementary, diagonals perpendicular, diagonals congruent, diagonals bisect)

everything is true

kite (properties; opp sides, opp angles, 2 consecutive angles supplementary, diagonals perpendicular, diagonals congruent, diagonals bisect)

Everything is false except diagonals are always perpendicular

right angle

an angle that is 90 degrees that is created by a perpendicular

bisector

a line that bisects another line, angle, segment, etc.

perpendicular

two lines that create a 90 degree angle