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

ASA (Angle-Side-Angle)

KD = 2/3 JD

The midsegment theorem

Points G and H trisect AB

Algebra

The diagonals of a parallelogram bisect each other

Algebra

AC = BC = BD = AD = AB

Substitution

< EAB = < FBA; < BAD = < ABD

Definition

ABCD is a parallelogram

Given

Definition

JK = 1/2 CK

Definition

Triangle AGD = Triangle BHD

AG + BH = 2/3 AB

CPCTC

ABCD is a rhombus

SAS (Side-Angle-Side)

Side-Splitter theorem

Angle addition theorem

Algebra

All rhombuses are parallelograms

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

An equilateral triangle is equiangular

CPCTC

Algebra

Algebra

JK = 1/2 KD

AG = GH = HB = 1/3 AB

EF || AB; EF = 1/2 AB

< EDA = < FDB

GH = 2/3 EF

Side-Splitter theorem

< EAD = < FBD

AK = KB; CK = KD

GH = 1/3 AB

Triangle EAD = Triangle FBD

AG = BH