Download Term - mrsjanellemaths

Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
Term
Example
Section 5-1
1
Symbol
Quadrilateral – a polygon
with four sides.
Parallelogram – a
quadrilateral with both pairs
of opposite sides parallel.
If a quadrilateral is a parallelogram then you know some important information:
Thrm. 5-1 – If a
quadrilateral is a
parallelogram, then its
opposite sides are
congruent.
Thrm. 5-2 – If a
quadrilateral is a
parallelogram, then its
opposite angles are
congruent.
Thrm. 5-3 – If a
quadrilateral is a
parallelogram, then its
diagonals bisect each other.
Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
Section 5-2
Term
Example
Symbol
If you know these facts, then you can prove a quadrilateral is a parallelogram:
Thrm. 5-4 – If both pairs of
opposite sides of a
quadrilateral are congruent,
then the quadrilateral is a
parallelogram.
Thrm. 5-5 – If one pair of
opposite sides of a
quadrilateral are congruent
AND parallel, then the
quadrilateral is a
parallelogram.
Thrm. 5-6 – If both pairs of
opposite angles of a
quadrilateral are congruent,
then the quadrilateral is a
parallelogram.
Thrm. 5-7 – If the
diagonals of a quadrilateral
bisect each other, then the
quadrilateral is a
parallelogram.
Hints on proving that a quadrilateral is a parallelogram:





Show both pairs of opposite sides are parallel (definition of a parallelogram)
Show both pairs of opposite sides are congruent (Thrm. 5-4)
Show that one pair of opposite sides are congruent and parallel (Thrm. 5-5)
Show both pairs of opposite angles are congruent (Thrm. 5-6)
Show that the diagonals bisect each other(Thrm. 5-7)
2
Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
Term
Thrm. 5-8 – If two lines are
parallel then all points on
one line are equidistant
from the other line.
Thrm. 5-9 – If three
parallel lines are cut off
congruent segments on one
transversal, then they cut of
congruent segments on
every transversal.
Thrm. 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.
(Midsegment)
Thrm. 5-11 – If a segment
joins the midpoints of two
sides of a triangle:
a) it is parallel to the
third side
b) it is half the measure
of the third side
Section 5-3
Example
Parallel Line Theorems
3
Symbol
Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
4
Section 5-4
RHOMBUS
4 congruent sides
RECTANGLE
4 right angles
How can you prove these are parallelograms?
Thrm. 5-12 – The diagonals of a rectangle are congruent.
Thrm. 5-13 – The diagonals of a rhombus are  .
Thrm. 5-14 – Each diagonal of a rhombus bisects a pair of
opposite angles.
SQUARE
4 congruent sides &
4 right angles
Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
Term
Thrm. 5-15 – The midpoint
of the hypotenuse of a right
triangle is equidistant from
the three vertices.
Example
Thrm. 5-16 – If an angle of
a parallelogram is a right
angle, then the
parallelogram is a rectangle.
Thrm. 5-17- If two
consecutive sides of a
parallelogram are
congruent, then the
parallelogram is a rhombus.
Section 5-5
Trapezoid – a quadrilateral with exactly one pair of parallel sides.
(special parts: bases, base angles, and legs)
5
Symbol
Honors Geometry – Regis Jesuit High School
Chapter 5 – Quadrilaterals
Isosceles Trapezoid – a
trapezoid where the legs are
congruent.
Thrm. 5-18 – Base angles
of an isosceles trapezoid are
congruent.
Median of a Trapezoid – a
segment that connects the
midpoints of the trapezoid’s
legs.
Thrm. 5-19 – The median
of a trapezoid:
a) is parallel to each
base
b) has a length equal to
the sum of the bases
divided by two.
6