Question

Write a paragraph proof of the Triangle Angle Sum Theorem using the following figure. A line should pass through F as part of the proof. I really need help... this is confusing me and I don't understand it. 30 POINTS if the answer is correct... don't just answer it because of the points. I will delete the answer and you won't get the points. PLEASE HELP!!!!!!!!!!!!!!!!!!!

Answer 1

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°.