Hnrs Geometry

Mainly just theorems for now

Isoceles Triangle

A triangle with at least two sides of equal length. The angles opposite these sides are also equal.

Base angles theorem

If two sides of a triangle are congruent, then the angles opposite then are congruent

Converse of the Base Angles Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Scalene Triangle

A triangle with all sides of different lengths and all angles of different measures.

Side-Angle-Side

(we know what this is) Just that the angle must be between the two sides.

Angle-Side-Angle

(also know this one) Just that the side must be between the two angles

Hypotenuse-Leg

Only for right triangles, need to prove they are right angles, that the hypotenuses are congruent and one of the sides are congruent

Parallel Postulate

If a point is not on the specific line then there can only be one line that can both go throught that point and be parallel to the specific line

Complementary angles

adds up to 90 degrees

Supplementary Angles

Adds up to 180 degrees

Alternate interior Angle theorem

The two alternate angles on the inside of the parallel lines will always be congruent (IF it is parallel)

Same-Side consecutive Interior angle theorem

If two lines are parallel and cut by a transversal, then the two angles on the inside of the parallel lines will be supplementary (IF the lines are parallel)

Alternate Exterior Angles theorem

Two angles on opposites sides of the transversal outside the parallel lines will be congurent (IF the lines are parallel)

Triangle angle sum theorem

The three angles in a triangle will always equal to 180 degrees.

Corresponding angle theorem

IF the two lines are parallel and cut by a transversal, then the two corresponding angles will always be congruent

Corresponding angles

Same side of the transversal will be supplementary

Collinear

What any anumber of points are if one straight line can connect them

substitution POE

if two quantities are equal, then one can be replaced by the other in any expression, equation, or geometric statement without changing its truth value

Addition POE

Adding the same number to both sides of an equation, keeping it balanced

Substitution POE

Subtracting the same number on both sides of an equation

Divison POE

Dividing the same number on both sides of an equation

Multiplacation POE

Multiplying the same number on both sides of an equation

Symmetric POE

if one quantity equals a second quantity, then the second equals the first

Transitive POE

If two values are equal to a third value, then the first two are equal

Congruent supllements theorem

if two angles are supplementary to the same angle (or to congruent angles), then those two angles are congruent to each other

Congruent compliments theorem

if two angles are complementary to the same angle (or to two congruent angles), then those two angles are congruent to each other

Corresponding angles theorem

Alternate interior angles theorem

Consecutive interior Angle Theorem

Alternate exterior angle theorem

Definition of Parallelogram (proving a parallelogram)

Show that both pairs of opposite sides are parallel

Parallelogram opposite sides converse (proving a parallelogram)

Show that both pairs of opposite sides are congruent

Parallelogram opposite angles converse (proving a parallelogram)

Show that both pairs of opposite angles are congruent

Opposite sides parallel and congruent theorem (proving a parallelogram)

Show that one pair of opposite sides are congruent and parallel

Parallelogram diagonals Converse (proving a parallelogram)

Show that the diagonals bisect each other

Finding the midsegment of a trapezoid

a + b/2 = midsegment

Isoceles Trapezoid Base Angles Theorem

If a trapezoid is isoceles, then each pair of base angles is congruent

Isoceles Trapezoid Base Angles Converse

If a trapezoid has a pair of congruent base angles, then it is an isoceles trapezoid

Isoceles Trapezoid Diagonals Theorem

A trapezoid is isoceles is and only if its diagonals are congruent

Kite Diagonals Theorem

If a quadrilateral is a kite, then its diagonals are perpendicular

kite opposite Angles Theorem

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent