Geometry proofs

Proofs

Addition property of equality

If a = b and c = d then a + c = b +d

Subtraction Property of equality

if a = b and c = d then a - c = b - d

Multiplication property of equality

if a = b then ca = cb

Division property of equality

if a = b and c ≠ 0, then a/c = b/c

Substitution property of equality

If a = b, then either a or b may be substituted for the other in any equation or inequality

Distributive property

a (b + c) = ab + ac or ab + ac = a (b + c)

Reflexive property of equality or congruence

m∠1 = m∠1

AB ≅ AB

Symmetric property of equality or congruence

m∠1 + m∠2 = m∠ 2 + m∠1

AB ≅ BA

Transitive property of equality or congruence

if a = b and b = c then a = c

If ∠A ≅ ∠B and ∠B ≅ ∠C then ∠A ≅ ∠ C

Supplementary

180

Complementary

90

Converse of corresponding angles theorem

If corresponding angles are equal, then the lines are parallel

Parallel postulate

through a point outside a line, exactly one parallel live can be drawn

Alternate exterior angles theorem

If lines are s alternate exterior angles are equal

Consecutive interior angles converse

If consecutive interior angles add up to 180°, the lines are parallel

Alternate interior angles converse

If alternate interior angles are equal lines are parallel

Perpendicular

Two lines that meet to form A 90°angle

Transversal converse

If A transversal creates certain equal or supplementary angles, then the lines are parallel

Corresponding

Same position, equal angles

Alternate interior

Inside the lines 1 opposite sides, equal angles

Alternate exterior

Outside the lines, opposite sides, equal angles

Consecutive interior

Inside the lines, same side, add up to 180°

Perpendicular #/2

Makes a square corner 90°

Parallel lines

Two cop/anar lines that don't intersect,

Skew lines

Lines that do not intersect and are not parallel

Parallel planes

Planes that do not intersect

Transversal

A line that intersects two or more lines in a plane at different points

Consecutive interior angles

Two interior angles on opposite sides of the transversal

Alternate exterior angles

Non adjacent exterior angles on opposite sides of the transversal

Corresponding angles

Two angles on the same side of transversal, one interior and one exterior angle

Corresponding angles theorem

If two parallel lines are cut by a transversal,then corresponding angles are congruent

Alternate interior angles theorem

If two parallel lines are cut by a transversal then, corresponding angles are congruent

Consecutive interior angles theorem -

If two parallel lines are cut by a transversals then consecutive interior angles are supplementary

,

Alternate exterior angles theorem

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent

Perpendicular transversal theorem

In a plane, if A line is perpendicular to one of two parallel lines, then it is perpendicular to the other

Two lines perpendicular to the same line are… parallel

Sometimes

Alternate interior angles are… congruent

Some times

Same-side interior angles are …. congruent

Sometimes

Same side interior angles are … supplementary

Sometimes

Two lines that do not intersect are… parallel

Sometimes

If x,y,z are collinear with Y between x and Z, then xy … equals xz -yz

Always