document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=793364>Question 793364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> are consecutive angles of a parallelogram called corresponding angles?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #480394 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=480394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I may call them consecutive interior angles. They are supplementary, meaning that their measures add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Usually we call corresponding angles the angles that \"are the same\" in one figure and another (usually triangles).<BR>\n" );
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document.write( "If the sides of triangles ABC and XYZ are congruent (the same length),<BR>\n" );
document.write( "with AB=XY, BC=YZ, and CA=ZX, we say that the triangles are congruent,<BR>\n" );
document.write( "and that sides AB and XY are corresponding sides.<BR>\n" );
document.write( "The same is said about the pairs of sides BC and YZ, and CA and ZX.<BR>\n" );
document.write( "The angles are also in pairs of corresponding angles (A with X, B with Y, C with Z), which are congruent (an important theorem in geometry).<BR>\n" );
document.write( "The fact that the sides are congruent means the triangles are congruent (they are the same triangle maybe moved, and/or rotated, and/or flipped).<BR>\n" );
document.write( "And the fact that triangles are congruent means that the corresponding angles are congruent, and you say that it is because of<BR>\n" );
document.write( "CPCTC = Congruent Parts of Congruent Triangles are Congruent.<BR>\n" );
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document.write( "Another case where we talk about corresponding angles is when we have two parallel lines intersected by a third line that we call a transversal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5%2C-2%2C5%2C-2%29%2Cline%28-5%2C2%2C5%2C2%29%2C%0D%0Aline%28-2%2C-5%2C2%2C5%29%2Clocate%280.5%2C2.5%2CA%29%2Clocate%281.1%2C2.5%2CB%29%2C%0D%0Alocate%280.3%2C2%2CC%29%2Clocate%280.9%2C2%2CD%29%2C%0D%0Alocate%28-1.1%2C-1.5%2CE%29%2Clocate%28-0.5%2C-1.5%2CF%29%2C%0D%0Alocate%28-1.3%2C-2%2CG%29%2Clocate%28-0.7%2C-2%2CH%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The pairs (A,E), (B,F), (C,G), and (Dd,H) are called corresponding, meaning that they are in the same position with respect to one parallel and the transversal.<BR>\n" );
document.write( "Corresponding angles are congruent there too.<BR>\n" );
document.write( "Other pairs of angles have special names too.<BR>\n" );
document.write( "Pairs that are opposed at the vertex, like (A,D) are called vertical. They are congruent too.<BR>\n" );
document.write( "Angles like A and H, outside the parallel lines and on alternate sides of the transversal, are called alternate exterior.  They are congruent too.<BR>\n" );
document.write( "Angles, like C and F, inside the parallel lines and on alternate sides of the transversal, are called alternate interior. They are congruent too.<BR>\n" );
document.write( "Pairs of angles like C and E, inside the parallel lines and on the same side of the transversal are called consecutive interior angles. They are supplementary, meaning that their measures add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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