Question

Use deductive reasoning to show that the two triangles are congruent. given that fab is congruent to ged and c is the midpoint of ae prove that abc is congruent to edc

Answer 1

ΔABC is congruent to ΔEDC by the Angle-Side-Angle congruency rule

Explanation:

The

Statement
`{}` Reason

∠FAB ≅ ∠GED
`{}` Given

C = Midpoint of
`\overline {AE}`
`{}` Given

∠BAC and ∠FAB are supplementary Angles on a straight line

∠DEC and ∠GED are supplementary Angles on a straight line

∠BAC ≅ ∠DEC
`{}` Transitive property

`\overline {AC}` ≅
`\overline {CE}`
`{}` Definition of midpoint

ΔABC ≅ ΔEDC
`{}` ASA congruency rule

Where two angles and an included side of one triangle is congruent to the corresponding two angles and an included side of another triangle, both triangles are congruent.
`{}`