Question

Given AB || DC and AC is the segment bisector of BD, complete the flowchartproof below. Note that the last statement and reason have both been filled in foryou. Triangle ABE is congruent to Triangle CDE, the reason is SAS.**there are also two 3 boxes that got cut off, they are the same as the first two.**

Answer 1

The flowchart to prove the congruence of the triangles ΔABE and ΔCDE can be presented as follows;

`\overline{AB}` ║
`\overline{DC}`
`\overline{AC}` is the segment bisector of
`\overline{BD}`

Given Given

↓ ↓

∠CDE ≅ ∠BAE
`\overline{DE}` ≅
`\overline{BE}`
`\overline{DC}` ≅
`\overline{BA}` Alt. int Angles Defn of bisected segment Congruence marking

↓ ↓ ↓

ΔABE ≅ ΔCDE

SAS

The completed statement and reasons can be presented in a tabular form as follows;

Statement Reasons

`\overline{AB}` ║
`\overline{DC}` Given

`\overline{AC}` ⊥ bisector of
`\overline{BD}` Given

`\overline{DC}` ≅
`\overline{BA}` Congruent segment marking

∠DCE ≅ ∠EAB Alternate interior angles

`\overline{DE}` ≅
`\overline{BE}` Definition of bisected segment

ΔCDE ≅ ΔABE Side Angle Side congruence rule