SAS (Side-Angle-Side)

The diagonals of a parallelogram bisect each other

Algebra

∠EAD = ∠FBD

Definition

AC = BC = BD = AD = AB

KD = 2/3 JD

An equilateral triangle is equiangular

EF ǁ AB; EF = 1/2 AB

Side-Splitter theorem

ABCD is a rhombus

Triangles ABC, ABD equilateral; E and F midpoints of AC, BC

∠EAB = ∠FBA; ∠BAD = ∠ABD

Points G and H trisect AB

AG + BH = 2/3 AB

△AGD ≅ △BHD

Algebra

Angle addition theorem

JK = 1/2 CK

All rhombuses are parallelograms

Algebra

GH = 2/3 EF

Side-Splitter theorem

Definition

The midsegment theorem

Definition

∠EAD = ∠EAB + ∠BAD; ∠FBD = ∠FBA + ∠ABD

CPCTC

ASA (Angle-Side-Angle)

AG = GH = HB = 1/3 AB

Substitution

Algebra

Algebra

∠EDA = ∠FDB

CPCTC

JK = 1/2 KD

Given

ABCD is a parallelogram

AK = KB; CK = KD

GH = 1/3 AB

△EAD ≅ △FBD

AG = BH