The reasons that can be used to complete the two column table used to prove the required expressions are;
1. ∆ABD Cong. ∆CBE Side-Angle-Side, SAS, rule of congruency
2. ∆ABC cong. ∆EDC Angle-Side-Angle, ASA, rule of congruency
<h3>Which postulates can be used to complete the tables?</h3>
1. Statements Reasons
1) <A = <C Given
2) AB = BC. Congruent sides of isosceles triangle
3) AE Cong. DC. Given
4) AE = DC. Definition of congruency
5) ED Cong. ED. Reflexive property of equality
6) AE + ED = DC + ED Addition property of equality
7) AE + ED = AD, DC + ED = CD Addition property of equality
8) AD = ED, Substitution property of equality
9) AD Cong. ED Definition of congruency
10) ∆ABD Cong. ∆CBE Side-Angle-Side, SAS, rule of congruency
2. Statements Reasons
1) AB || DE Given
Midpoint of BD = C Given
2) <ABC Cong. <EDC Alternate angles formed by parallel lines
3) BC Cong. CD Definition of midpoint
4) <ACB Cong. <DCE Vertical angle theory
5) ∆ABC cong. ∆EDC Angle-Side-Angle, ASA, rule of congruency
Learn more about the rules of congruency here:
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