The statements and reasons to prove that [tex]\overline{DE}[/tex] [tex]\cong[/tex] [tex]\overline{CE}[/tex] are presented as
follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{AD}[/tex] [tex]\cong[/tex] [tex]\overline{BC}[/tex] [tex]{}[/tex] 1. Given
2. ∠BCD ≅ ∠ADC [tex]{}[/tex] 2. Given
3. [tex]\overline{DC}[/tex] [tex]\cong[/tex] [tex]\overline{DC}[/tex] [tex]{}[/tex] 3. Reflective property
4. ΔADC ≅ ΔBCD [tex]{}[/tex] 4. By SAS rule of congruency
5. ∠DAE ≅ ∠CBE [tex]{}[/tex] 5. By CPCTC
6. ∠AED ≅ ∠BEC [tex]{}[/tex] 6. By vertical angles theorem
7. ΔAED ≅ ΔBEC [tex]{}[/tex] 7. By SAA rule of congruency
8. [tex]\overline{DE}[/tex] [tex]\cong[/tex] [tex]\overline{CE}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. By CPCTC
The abbreviations are;
SAS; Side-Angle-Side rule of congruency, which states that two triangles
are congruent if their corresponding two sides and included angle are
congruent.
CPCTC; Congruent Parts of Congruent Triangle are Congruent, which is
the rule that if two figures are congruent, their corresponding parts are
also congruent.
SAA; Side-Angle-Angle rule of congruency which states that two triangles
are congruent if they each have two angles and a corresponding adjacent
side that are equal.
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