document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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\r
\n" ); document.write( "\n" ); document.write( "The figure shows a polygon comprised of three triangles, ABC, CEG, and DFE.
\n" ); document.write( "Prove ΔABC ∼ ΔGEC. \n" ); document.write( "

Algebra.Com's Answer #843449 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "given: Δ $\"ABC\"$ ≅ Δ $\"DEF\"$
\n" ); document.write( "Prove Δ $\"ABC\"$ ∼ Δ $\"GEC\"$ \r
\n" ); document.write( "\n" ); document.write( "we need to show that the corresponding angles of these triangles are congruent\r
\n" ); document.write( "\n" ); document.write( "statement...................................reason
\n" ); document.write( "Δ $\"ABC\"$ ≅ Δ $\"DEF\"$ ........................given (all their corresponding angles are congruent)
\n" ); document.write( "< $\"ABC\"$ ≅ < $\"GEC\"$ ........................point $\"+C\"$ is the intersection of lines $\"AG+\"$ and $\"BE\"$ , and $\"GC\"$ || $\"+DF\"$ , Alternate Interior Angles Theorem\r
\n" ); document.write( "\n" ); document.write( "< $\"DEF\"$ ≅ < $\"GCE\"$ ......................point $\"E+\"$ is the intersection of lines $\"DG\"$ and $\"BF\"$ , and $\"CG\"$ || $\"DF\"$ , Alternate Interior Angles Theorem
\n" ); document.write( " Δ $\"ABC\"$ ∼ Δ $\"GEC\"$ .....................by the angle-angle ( $\"AA\"$ ) theorem\r
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