SOLUTION: In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF , while point E is the point of intersection between segment DG and seg

Algebra ->  Geometry-proofs -> SOLUTION: In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF , while point E is the point of intersection between segment DG and seg      Log On


   

Question 1206184: In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF , while point E is the point of intersection between segment DG and segment BF.
https://api.agilixbuzz.com/Resz/~0.Bv8W_aJ6tRosNuyK.A.WQX-LKs4_7CtNbGXeaKp1TM-Q57bSJTC4440BKyZad8/196638831,F41,1,15,0,30,0,3/Assets/94559_55a90aae/05_08_1b.gif
The figure shows a polygon comprised of three triangles, ABC, CEG, and DFE.
Prove ΔABC ∼ ΔGEC.
Answer by MathLover1(20850) About Me  (Show Source):
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given: ΔABC ≅ ΔDEF
Prove ΔABC ∼ ΔGEC
we need to show that the corresponding angles of these triangles are congruent
statement...................................reason
ΔABC ≅ ΔDEF........................given (all their corresponding angles are congruent)
< ABC ≅ <GEC........................point+C is the intersection of lines AG+and BE, and GC ||+DF, Alternate Interior Angles Theorem
< DEF ≅ < GCE......................point E+is the intersection of lines DG and BF, and CG || DF, Alternate Interior Angles Theorem
ΔABC ∼ ΔGEC.....................by the angle-angle (AA) theorem