Proofs Notes

Linear Pair Postulate (LPP)

• States that if the measure of two angles adds up to 180°, they are considered complementary.

Segment Addition Postulate (SAP)

• States that if point B lies on line AC and is situated between points A and C, then the sum of the lengths of segments AB and BC equals the length of segment AC.

  • Formula: AB + BC = AC

Angle Addition Postulate (AAP)

• States that if point D lies on the interior of angle ABC, then the measure of angle ABD plus the measure of angle DBC equals the measure of angle ABC.

  • Formula: m∠ABD + m∠DBC = m∠ABC

Triangle Congruence Postulates

Side-Side-Side (SSS) Congruence

• States that if three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence

• States that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.