SOLUTION: Given: Quadrilateral ABCD Segment AC bisects angle DAB Segment DB bisects angle ADC Segment AB is parallel to segment DC Prove: ABCD is a rhombus

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Question 1209431: Given: Quadrilateral ABCD
Segment AC bisects angle DAB
Segment DB bisects angle ADC
Segment AB is parallel to segment DC
Prove: ABCD is a rhombus
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let point E represent the intersection of diagonals AC and BD.

I'll provide a portion of the proof table.
NumberStatementReason
1Segment AC bisects angle DABGiven
2Segment DB bisects angle ADCGiven
3Segment AB is parallel to segment DCGiven
4Angle DAC = Angle CABDefinition of Angle Bisection
5Angle ADB = Angle CDBDefinition of Angle Bisection
6Angle CAB = Angle ACDAlternate Interior Angles
7Angle DAC = Angle ACDTransitive Property
8Segment DE = Segment DEReflexive Property
9Triangle AED = Triangle CEDAAS Congruence Theorem
10Segment AD = Segment DCCPCTC

I'll let the student finish up from here.
The goal is to show that AB = BC = CD = AD.
So far the proof table above has demonstrated that AD = DC.

Abbreviations:
AAS = angle angle side
CPCTC = corresponding parts of congruent triangles are congruent
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