Chapter 5 Flashcards
Indirect Proof
A proof where the givens or another
known fact is proven wrong, thus
contradicting itself and proving the to
prove correct. Start by assuming the to
prove negative. End by using def of
contradiction and finally law of
contradiction.
The Exterior Angle
Inequality Theorem
Thm: The measure of a exterior angle of
a triangle is greater than the measure of
either remote interior angles.
Alt int.
Thm: If two lines are cut by a transversal
such that two alternate interior angles are
congruent, the lines are parallel. Alt int <s
≅ ⇒ Parallel lines
Alt ext.
Thm: If two lines are cut by a transversal
such that two alternate exterior angles
are congruent, the lines are parallel. Alt
ext <s ≅ ⇒ Parallel lines
Corr
Thm: If two lines are cut by a transversal
such that two corresponding angles are
congruent, the lines are parallel.
corresponding <s ≅ ⇒ Parallel lines
SS int
Thm: If two lines are cut by a transversal
such that two interior angles on the same
side of the transversal are
supplementary, the lines are parallel. SS
int <s supp ⇒ Parallel lines
SS ext
Thm: If two lines are cut by a transversal
such that two exterior angles on the same
side of the transversal are
supplementary, the lines are parallel. SS
ext <s supp ⇒ Parallel lines
Coplanar
Thm: If two coplanar lines
are perpendicular to a third
line, they are parallel.
The Parallel
Postulate
Post: Through a point not
on a line there is exactly
one parallel to the given
line.
Converse of alt int
Thm: If two parallel lines are cut by a
transversal, each pair of alternate interior
angles are congruent. Parallel Lines ⇒ alt
int <s ≅
Congruent or Supp
Thm: If two parallel lines are cut by a
transversal, then any pair of the angles
formed are either congruent or
supplementary. Parallel Lines ⇒ <s ≅ or
supp
Converse of alt ext
Thm: If two parallel lines are cut by a
transversal, each pair of alternate exterior
angles are congruent. Parallel Lines ⇒ alt
ext <s ≅
Converse of Corr
Thm: If two parallel lines are cut by a
transversal, each pair of corresponding
angles are congruent. Parallel Lines ⇒
corr <s ≅
Converse of SS int
Thm: If two parallel lines are cut by a
transversal, each pair of interior angles
on the same side of the transversal are
supplementary. Parallel Lines ⇒ ss int <s
supp
Converse of SS ext
Thm: If two parallel lines are cut by a
transversal, each pair of exterior angles
on the same side of the trasversal are
supplementary.Parallel Lines ⇒ ss ext <s
supp
Perp to one, perp to
other
Thm: In a plane, if a line is perpendicular
to one of two parallel lines, it is
perpendicular to the other. ⊥ to one
parallel line ⇒ ⊥ to other
Transitive Prop of
Parallel lines
Thm: If two lines are
parallel to a third line, then
they are parallel to each
other.
Polygon
Def: plane figures that consist entirely of
segments, with no nonconsecutive sides
intersecting, and each vertex only
belonging to two sides.
Convex Polygon
Def: A polygon in which
each interior angle has a
measure less than 180°
Diagonal
Def: Any segment that
connects two
nonconsecutive vertices of
the polygon.
Parallelogram
Def: A quadrilateral in
which both pairs of
opposite sides are parallel.
Quadrilateral
Def: A four sided
polygon.
Rectangle
Def: A parallelogram in
which t least one angle is a
right angle.
Rhombus
Def: A parallelogram in
which at least two
consecutive sides are
congruent.
Square
Def: A parallelogram that is
both a rectangle and a
rhombus.
Kite
Def: A quadrilateral in
which two distinct pairs of
consecutive sides are
congruent.
Trapezoid
Def: A quadrilateral with exactly one pair
of parallel sides. The parallel sides are
called bases of the trapezoid.
Isosceles Trapezoid
Def: A trapezoid in which
the nonparallel sides (legs)
are congruent.
Properties of a
Parallelogram
1. Def: The opposite sides are parallel2.
Thm: The opposite sides are congruent3.
Thm: The opposite angles are
congruent4. Thm: Any pair of consecutive
angles are supplementary
Properties of a
Rectangle
1. Def: All properties of a parallelogram
apply2. Thm: All angles are right angles3.
The diagonals are congruent
Properties of a Kite
1. Def: two disjoint pairs of consecutive
sides are congruent2. Thm: The
diagonals are perpendicular3. Thm: One
diagonals is the perpendicular bisector of
the other4. Thm: One of the diagonals
bisects a pair of opposite angles5. Thm:
One pair of opposite angles are
congruent
Properties of a
Rhombus
1. Def: All the properties of a
parallelogram2. Thm: All the properties of
a kite apply 3. Thm: All the sides are
congruent, equilateral 4. Thm: The
diagonals bisect the angles5. Thm: The
diagonals are perpendicular bisectors6.
Thm: The diagonals divide the rhombus
into 4 congruent right triangles
Properties of a
Square
1. Def: All the properties of a rectangle
apply2. Def: All the properties of a
rhombus apply3. Thm: The diagonals
form four right triangles (45-45-90)
Properties of an
Isosceles Trapezoid
1. Def: The legs are congruent2. Def: The
bases are parallel3. Thm: The lower base
angles are congruent4. Thm: The upper
base angles are congruent5. Thm: The
diagonals are congruent6. Thm: Any
lower base angle is supplementary to any
upper base angle
How to prove a
quadrilateral is a
parallelogram
1. Thm: If both pairs of opposite sides of
a quadrilateral are parallel, then it is a
parallelogram. 2. Thm: If both pairs of
opposite sides of a quadrilateral are
congruent, then it is a parallelogram.3.
Thm: If one pair of opposite sides are
both congruent and parallel, then it is a
parallelogram.4. Thm: If the diagonals of
a quadrilateral bisect each other, then it is
a parallelogram. 5. Thm: If both pairs of
opposite angles of a quadrilateral are
congruent, then it is a parallelogram.
How to prove a
quadrilateral is a Rectangle
1. Def: If a parallelogram contains at least
one right angle, then it is a rectangle.2.
Thm: If the diagonals of a parallelogram
are congruent, ''3. Thm: If all four angles
of a quadrilateral are right angles, ''
How to prove a
quadrilateral is a
Kite
1. Thm: If 2 disjoint pairs of consecutive
sides of a quadrilateral are congruent ,
then it is a kite. 2. Thm: If one of the
diagonals of a quadrilateral is the
perpendicular bisector of the other
diagonal, ''.
How to prove a
quadrilateral is a Rhombus
1. Thm: If a parallelogram contains a pair
of consecutive sides that are
congruent...2. Thm: If either diagonal of a
parallelogram bisects two angles of the
parallelogram...3. Thm: If the diagonals of
a quadrilateral are perpendicular
bisectors of each other...
How to prove a
quadrilateral is a Square
Thm: If a quadrilateral is
both a rectangle and a
rhombus, then it is a
square.
How to prove a
trapezoid is a
isosceles
1. Thm: If the nonparallel sides of the
trapezoid are congruent2. Thm: If the
lower or the upper base angles of a
trapezoid are congruent3. Thm: If the
diagonals of a trapezoid are congruent