Geometry Test #6 Flashcards
Distance Formula
d = √((x2 - x1)^2 + (y2 - y1)^2)
Slope Formula
m = (y2 - y1) / (x2 - x1)
Midpoint Formula
(x1 + x2)/2, (y1 + y2)/2
Slope-Intercept Form
y = mx + b (m is the slope, b is the y-intercept)
Point-Slope Form
y - y1 = m(x - x1)
(m is the slope, (x1, y1) is a point on the line)
Standard Form
Ax + By = C (A, B, C are constants)
Parallelogram
opposite sides are parallel and equal in length
Rectangle
four right angles and opposite sides are equal in length
Rhombus
all sides are equal in length and opposite angles are equal
Square
four right angles and all sides are equal in length
Trapezoid
exactly one pair of opposite sides are parallel
Ways of Proving Congruent Triangles:
SSS
SAS
ASA
AAS
HL (for right angles)
CPCTC
Corresponding parts of congruent triangles are congruent
Isosceles Triangle Definition
A triangle that has at least 2 congruent sides
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite them are congruent.
Median
connects a vertex of a triangle to the midpoint of the opposite side.
Altitude
connects a vertex of a triangle to the opposite side and is perpendicular to it.
Angle Bisector
divides an angle into two congruent angles.
Perpendicular Bisector
bisects a line segment and is perpendicular to it.
Medians
Centroid
Altitudes
Orthocenter
perpendicular bisectors
Circumcenter
angle bisectors
Incenter
Opposite sides of a ____ are congruent.
Opposite sides of a parallelogram are congruent
Opposite angles of a ___ are congruent
Opposite angles of a parallelogram are congruent
Diagonals of a parallelogram ___ each other
Diagonals of a parallelogram bisect each other
If both pairs of a quadrilateral are congruent, then the quadrilateral is a ___
If both pairs of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a ___.
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a __.
If both pairs of opposite angles of a parallelogram are congruent, then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a __.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
If two lines are parallel, then all points on one line are __ from the other line.
If two lines are parallel, then all points on one line are equidistant from the other line.
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
The segment that joins the midpoints of two sides of a triangle…
(1) is parallel to the third side
(2) is half as long as the third side.
The segment that joins the midpoints of two sides of a triangle…
(1) is parallel to the third side
(2) is half as long as the third side
The diagonals of a rectangle are __.
The diagonals of a rectangle are congruent.
The diagonals of a rhombus are __.
The diagonals of a rhombus are perpendicular.
Each diagonal of a rhombus _______.
Each diagonal of a rhombus bisects two angles of the rhombus.
The midpoint of the hypotenuse of a right triangle is __ from the three vertices.
The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
The midpoint of the hypotenuse of a right triangle is __ from the three vertices.
The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
If an angle of a __ is a right angle, then the __ is a __.
If the angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
If two consecutive sides of a __ are congruent, then the __ is a __.
If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
Base angles of an ___ are congruent.
Base angles of an isosceles trapezoid are congruent.
