Answer:
Step-by-step explanation:
To prove the triangle angle sum theorem,
We will do a construction by drawing a line PQ passing through point F and parallel to line DE.
Statements Reasons
1). ∠PFD + ∠QFD = 180° 1). linear pair postulate
2). ∠QFD = ∠QFE + ∠EFD 2). Angle addition postulate
3). ∠PFD + ∠QFE + ∠EFD = 180° 3). Substitution property
4). ∠PFD ≅ ∠FDE 4). Alternate interior angles
∠QFE ≅ ∠DEF
5). ∠FDE + ∠DEF + ∠EFD = 180° 5). Substitution property
Hence sum of interior angles of ΔDEF is 180°.
