geometry: chapter 5 Flashcards
Parallelogram
A quadrilateral with both pairs of opposite sides parallel
Quadrilateral
A four sided polygon
Theorem 5-1
Opposite sides of a parallelogram are congruent
Theorem 5-2
Opposite angles of a parallelogram are congruent
Theorem 5-3
Diagnose of a parallelogram bisect each other
Theorem 5-4
If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram
Theorem 5-5
If one pair of opposite sides of a quadrilateral are both congruent and parallel than the quadrilateral is a parallelogram
Theorem 5-6
If both pairs of opposite sides of a quadrilateral are congruent than the quadrilateral is a parallelogram
Theorem 5-7
If the diagonals of a quadrilateral bisect each other than the quadrilateral is a parallelogram
Five ways to prove that a quadrilateral is a parallelogram
show that both pairs of opposite sides are parallel
Show that both pairs of opposite sides are congruent
Show that one pair of opposite sides are both congruent and parallel
Show that both pairs of opposite angles are congruent
Show that the diagonals bisect each other
Theorem 5-8
If two lines are parallel then all points on one line are equidistant from the other one
Theorem 5-9
If three parallel lines cut off congruent segments on one transversal then they cut off congruent segments on every transversal
Theorem 5-10
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
Theorem 5-11
The segment that joins the midpoint of two sides of a triangle is
Parallel to the third side
Half as long is the third
Rectangle
A quadrilateral with four right angles
Rhombus
Quadrilateral with four congruent sides
Square
A quadrilateral with four right angles and four congruence
Theorem 5-12
The diagonals of a rectangle are congruent
Theorem 5-13
The diagonals of around this are perpendicular
Theorem 5-14
Each diagonal of a rhombus bisects two angles of the rhombus
Theorem 5-15
The midpoint of the hypotenuse of a right triangle is equidistant from three vertices
Theorem 5-16
if an angle of the parallelogram is a right angle then the parallelogram is a rectangle
Theorem 5-17
If two consecutive sides of a parallelogram are congruent then parallelogram is a rhombus
Trapezoid
Why gelato with exactly one pair of parallel sides
Bases
The parallel sides of the trapezoid
Legs
The other side of the trapezoid
Isosceles trapezoid
A trapezoid with congruent legs
Theorem 5-18
Base angles of an isosceles trapezoid are congruent
Median of a trapezoid
Segment that joins the midpoint of the legs
Theorem 5-19
Median of a trapezoid
Is parallel to the bases
Has a length equal to the average of the base lengths
