Question

Write a proof in paragraph format.

Given: AE←→
is the ⊥
bisector of BC¯¯¯¯¯¯¯¯
; BE←→
is the ⊥
bisector of AD¯¯¯¯¯¯¯¯

Prove: CA=DB

Answer 1

The paragraph method to prove CA = Db can be presented as follows;

Since
`\overleftrightarrow{AE}` is the ⊥ bisector of
`\overline{BC}`;
`\overleftrightarrow{BE}` is the ⊥ of
`\overline{AD}`, therefore, the perpendicular bisector theorem indicates that
`\overline{AB}` ≅
`\overline{CA}` and
`\overline{AB}` ≅
`\overline{DB}` and the transitive property of congruence indicates that we get
`\overline{CA}` ≅
`\overline{DB}`, from which, based on the definition of congruent segments, we get CA = DB

The details of the theorems, properties and definition used to prove the equivalence of the segments CA and DB can be presented as follows;

• The perpendicular bisector theorem states that a point on the perpendicular bisector of a segment is equidistant from the boundaries points of the segments

• The transitive property of congruence states that if A ≅ B, and A ≅ C, then, B ≅ C

• Congruent segments are segments that have the same lengths