Possible Reasons That Can Be Used for Triangle Congruence Proofs

Altitude

Is a line segment drawn from a vertex perpendicular to the opposite side.

Median

Is a line segment drawn from a vertex to the midpoint of the opposite side.

Angle bisector

Is a line segment or ray drawn from a vertex that cuts the angle in half.

Perpendicular

Perpendicular lines form congruent right triangles

Midpoint

Forms 2 congruent segments

Segment  bisector

Forms 2 congruent segments

Regular polygon

Convex polygon with all sides congruent and all angles congruent

Parallelogram

A quadrilateral with both pairs of opposite sides parallel

Rhombus

A parallelogram with 4 congruent sides

Rectangle

A parallelogram with 4 right angles

Square

A parallelogarm with 4 right angles and 4 congruent sides

Trapezoid

A quadrilateral with one pair of opposite sides parallel

Isosceles Trapezoid

A trapezoid with a pair of congruent legs.

Linear Pair Postulate

Linear Pair Angles are supplementary

Reflexive property

Shared side/angle, congruent to itself

Corresponding Angles Postulate

When parallel lines are cut by a transversal, corresponding angles are congruent,

Transversal

Of a line intersecting a system of lines

Converse of corresponding Angles Postulate

When two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Addition property of equality.

Equals + equals = equals

Halves of equals

½ of equals are equals

Segment Addition Postulate

This means that if you have a line segment divided into smaller, adjacent segments, you can find the total length by adding the lengths of the smaller parts

Angle Addition Postulate

if a ray divides an angle into two adjacent angles, the measure of the larger angle is the sum of the measures of the two smaller angles

Triangle Sum Theorem

The sum of all interior angles in a triangle is 180 degrees.

Exterior Angle Theorem

Exterior angle measure equals the sum fo the two remote interior angles’ measures.

Vertical Angle Theorem

Vertical Angles are congruent.

CPCTC

Corresponding parts of congruent triangles are congruent.

Perpendicular Biesctor Theorem

Any point on the perpendicular bisector is equidistant form the endpoints of the segment bisected.

Alternate Interior Angles Theorem

When parallel lines are cut by a transversal, alternate interior angles are congruent.

Converse of Alternate Interior Angles Theorem

When two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Same Side Interior Angles Theorem

When parallel lines are cut by a transversal, same side interior angles are supplementary.

Isosceles Triangle Theorem (ITT)

The base angles of an isosceles triangle are congruent

Converse Isosceles Triangle Theorem (CITT)

If the base angles in a triangle are congruent then the triangle is isosceles

Properties of rectangle

All properties of parallelograms and diagonals are congruent

Properties of rhombus

All properties of parallelograms and diagonals are perpendicular, diagonals bisect vertices of the polygon.

Properties of square

All properties of parallelograms, rectangles, and rhombuses.