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Geometry
Geometry Proofs
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Geometry Proofs
Terms in this set (69)
Segment Addition Postulate
If three points A, B, C are collinear and B is between A and C, then AB+BC=AC
Definition of a Congruent Segment
Segments that have the same length (Used when you switch from an "=" sign to a "≅" sign or vice versa)
Definition of a Segment Bisector
a line, segment, ray, or plane that intersects a segment at its midpoint the segment into two congruent segments
Definition of a Midpoint
divides the segment into two congruent segments
Angle Addition Postulate
If point B is in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC
Definition of Complementary Angles
two angles whose degree measures have a sum of 90º
Definition of Supplementary Angles
two angles whose degree measures have a sum of 180º
Vertical Angles
are always congruent and you can assume from a picture
Definition of a Linear Pair
you can assume from a picture
Linear Pair Postulate
are always supplementary
Definition fo an Angle Bisector
a segment that divides an angle into two congruent angles; intersects at midpoint
Law of Detachment
p->q
p
q
Law of Syllogism
p->q
q->r
p->r
Reflexive Property of Equality
a=a
Symmetric Property of Equality
a=b, b=a; 8=x, x=8
Transitive Property of Equality
a=b, b=c, a=c [usually not = to a #]
Addition Property of Equality
a+c=b+c
Subtraction Property of Equality
a-c=b-c
Multiplication Property of Equality
a(c)=b(c)
Division Property of Equality
c ≠0, a/c=b/c
Substitution Property of Equality
AB=8, BC=8, AB=BC
Distributive Property of Equality
a(b+c)=ab+ac
Angles Supplementary to the Same Angle
are congruent
Angles Supplementary to Congruent Angles
are congruent
Angles Complementary to the Same Angle
are congruent
Angles Complementary to Congruent Angles
are congruent
If Two Angles are Congruent and Supplementary
then each is a right angle
All Right Angles
are congruent
Definition of Perpendicular Lines
form four right angles
Definition of a Right Angle
measures 90º
Same Side Interior Angles Postulate
two parallel lines that are same side interior angles are supplementary
Alternate Interior Angles Theorem
two parallel lines that are alternate interior angles are congruent
Corresponding Angles Theorem
two parallel lines that are corresponding angles are congruent
Alternate Exterior Angles Theorem
two parallel lines that are alternate exterior angles are congruent
Converse of Same Side Interior Angles
if the converse of same side angles are supplementary, then the lines are parallel
Converse of Alternate Interior Angles Theorem
if the alternate interior angles are congruent, then the lines are parallel
Converse of Corresponding Angles Theorem
if the corresponding angles are congruent, then the lines are parallel
Converse of Alternate Exterior Angles Theorem
if the alternate exterior angles are congruent, then the lines are parallel
Two lines parallel to the same line
are parallel to each other
Two lines perpendicular to the same line
are parallel to each other
Perpendicular Transversal Theorem
if a line is perpendicular to one of the two lines, then it is perpendicular to the other
Angle Sum Theorem
the sum of the measures of the angles of a triangle is 180
Exterior Angle Theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
Definition of Slope
m= rise
------
run
Third Angles Theorem
if two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
SSS Postulate
(Side-Side-Side) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
SAS Postulate
(Side-Angle-Side) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
ASA Postulate
(Angle-Side-Angle) If two angles and the
included
side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
AAS Theorem
(Angle-Angle-Side) If two angles and a
nonincluded
side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.
Definition of Congruent Triangles
(CPCTC) Two triangles are congruent if and only if their congruent corresponding parts are congruent
Definition of Isosceles Triangle
a triangle that has two congruent sides
Isosceles Triangle Theorem
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
Converse Isosceles Triangle Theorem
if two angles of a triangle are congruent, then the sides opposite of those angles are congruent
If a line bisects the vertex angle of an isosceles triangle
then the line is also the perpendicular bisector of the base
A triangle is an equilateral
if and only if it is equiangular. Each angles of an equilateral triangle measures 60 degrees.
Hypotenuse Leg Theorem
if the hypotenuse and leg of one triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent
A triangle is equilateral if and only if it is _____.
equiangular
Definition of a Parallelogram
If a quadrilateral is a parallelogram, then the quadrilateral's both pairs of opposite sides are parallel
(1/5 Characteristic of a Parallelogram)
If a quadrilateral is a parallelogram, then the opposite sides are _____.
congruent
(2/5 Characteristic of a Parallelogram)
If a quadrilateral is a parallelogram, then the opposite angles are _____.
congruent
(3/5 Characteristic of a Parallelogram)
If a quadrilateral is a parallelogram, then the consecutive angles are _____.
supplementary
(4/5 Characteristic of a Parallelogram)
If a quadrilateral is a parallelogram, then the diagonals _____.
bisect each other
(5/5 Characteristic of a Parallelogram)
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on _____.
every transversal
If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a _____.
parallelogram
If both pairs of opposite of sides of a quadrilateral are congruent, then the quadrilateral is a _____.
parallelogram
If both pairs of opposite of angles of a quadrilateral are congruent, then the quadrilateral is a _____.
parallelogram
If diagonals of a quadrilateral bisect each other, then the quadrilateral is a ______.
parallelogram
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a _____.
parallelogram
If the consecutive interior angles are supplementary, then the quadrilateral is a _____.
parallelogram
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