ABCD is a rhombus

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

GH = 2/3 EF

EF ǁ AB; EF = 1/2 AB

Algebra

Algebra

Definition

Side-Splitter theorem

AC = BC = BD = AD = AB

CPCTC

KD = 2/3 JD

ASA (Angle-Side-Angle)

CPCTC

Side-Splitter theorem

The diagonals of a parallelogram bisect each other

An equilateral triangle is equiangular

Algebra

Angle addition theorem

AG = GH = HB = 1/3 AB

Substitution

Given

All rhombuses are parallelograms

JK = 1/2 CK

Points G and H trisect AB

JK = 1/2 KD

∠EDA = ∠FDB

AG + BH = 2/3 AB

Algebra

Definition

Algebra

ABCD is a parallelogram

The midsegment theorem

△AGD ≅ △BHD

Definition

SAS (Side-Angle-Side)

∠EAB = ∠FBA; ∠BAD = ∠ABD

∠EAD = ∠FBD

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

AK = KB; CK = KD

GH = 1/3 AB

△EAD ≅ △FBD

AG = BH