Given That C Is The Midpoint Of Line Ae And Line Bd, Prove That 0394abc 2245 0394edc.

Given that C is the midpoint of line AE and line BD, prove that ΔABC ≅ ΔEDC.

 

Answer:

ΔABC ≅ ΔEDC

Proof: SAS Theorem (Side-Angle-Side)

Step-by-step explanation:

Statement: C is the midpoint of AE and BD

Proof: Given

Statement:  AE bisects BD; BD bisects AE

Proof:  Segment bisector definition

Statement: AC ≅ CE and BC ≅ CD

Proof: Definition of Midpoint

Statement: ∠ACB ≅ ∠DCE

Proof: Vertical Angles are congruent

Statement: AB ≅ DE

Proof: Symmetry Property

Statement: ΔABC ≅ ΔEDC

Proof: CPCTC (Congruent Parts of Congruent Triangle are Congruent)

Statement:  ΔABC ≅ ΔEDC

Proof: SAS Theorem (Side-Angle-Side)

SAS Theorem: If two sides and included angle of one triangle (ΔABC) are congruent to two sides and included angle of another triangle (ΔEDC), then the two given triangles are congruent.

Please click the image below to view my illustration of the triangles based on given description.