Math Theoroms

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Exterior Angle Theorem (EAT)

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles

linear pair of angles (LPP)

linear pair angles are supplementary

Definition of Congruence

m∠A = m∠B ←→ ∠A ≅ ∠B

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Halves of Equals

1/2 of equals are equals

Converse of the Corresponding Angles Postulate

If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.

Angle Addition Postulate

for any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts

Reflexive Property

a shared side or angle, congruent to itself

Corresponding Angles Postulate

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

linear pair (angles)

two adjacent angles whose sum is a straight angle

triangle sum theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Exterior Angle Theorem (EAT)

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles

Vertical Angles Theorem (VAT)

Vertical angles are congruent

CPCTC

corresponding parts of congruent triangles are congruent

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Alternante Exterior Angles Theorem

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

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Converse of the Same-Side Interior Angles Theorem

If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.

Isosceles Triangle Theorem (ITT)

The base angles of an isosceles triangle are congruent

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent then the triangle is Isosceles

Properties of a rectangle

all properties of a parallelogram, all angles are right, diagonals are congruent

Properties of a Rhombus

1. ALL parallelogram properties apply

2. All Sides are congruent

3. Diagonals are perpendicular

4. Diagonals bisect angles

Property of Square

All properties of parallelograms, rectangles, and rhombuses