By addition property, equal areas subtracted from congruent triangles, form two other congruent triangles
[tex]\overline {DE}[/tex] ≅ [tex]\overline {CE}[/tex] by Congruent Parts of Congruent Triangles are Congruent, (CPCTC)
The reason the above proof is correct is given as follows;
The given parameters are;
[tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] and ∠BCD ≅ ∠ADC
Required:
Prove: [tex]\overline {DE}[/tex] ≅ [tex]\overline {CE}[/tex]
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] [tex]{}[/tex] Given
∠BCD ≅ ∠ADC [tex]{}[/tex] Given
[tex]\overline {DC}[/tex] ≅ [tex]\overline {DC}[/tex] [tex]{}[/tex] Reflective property
ΔADC ≅ ΔBDC [tex]{}[/tex] SAS rule of congruency
[tex]\overline {AB}[/tex] ≅ [tex]\overline {AB}[/tex] [tex]{}[/tex] Reflective property
ΔABD ≅ ΔABC [tex]{}[/tex] SSS rule of congruency
ΔABD = ΔABE + ΔAED [tex]{}[/tex] Addition property
ΔABC = ΔABE + ΔBEC [tex]{}[/tex] Addition property
Therefore;
ΔAED = ΔBEC [tex]{}[/tex] By converse of addition property
ΔAED ≅ ΔBEC [tex]{}[/tex] Definition of congruency
[tex]\overline {DE}[/tex] ≅ [tex]\overline {CE}[/tex] [tex]{}[/tex] By CPCTC
The acronyms used in the proof are;
SAS: Side Angle Side rule of congruency
CPCTC: Congruent Parts of Congruent Triangles are Congruent
SSS: Side-Side-Side rule of congruency
Learn more about CPCTC here:
https://brainly.com/question/2166368
