document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548932>Question 548932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a little trouble with trying to figure this problem out<BR>\n" );
document.write( "Given: Isos. Triangle STU <BR>\n" );
document.write( "ST is congruent to TU<BR>\n" );
document.write( "V is the midpoint of SU<BR>\n" );
document.write( "Prove: a)triangle svt is congruent to triangle uvt<BR>\n" );
document.write( "B)tv is perpendicular to su<BR>\n" );
document.write( "C)tv bisects angle stu<BR>\n" );
document.write( "D) angle s is congruent to angle u<BR>\n" );
document.write( "All I can get is:<BR>\n" );
document.write( "ST is congruent to TU:Given<BR>\n" );
document.write( "V is the midpoint of SU:Given<BR>\n" );
document.write( "SV is congruent to VU:Def. Of midpoint<BR>\n" );
document.write( "I'm stuck on what to do next.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357377 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You said:<BR>\n" );
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document.write( "ST is congruent to TU: Given <--- Good<BR>\n" );
document.write( "V is the midpoint of SU: Given <--- Good<BR>\n" );
document.write( "SV is congruent to VU: Def. Of midpoint <--- Good<BR>\n" );
document.write( "I'm stuck on what to do next.<BR>\n" );
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document.write( "If you can prove part A) triangle SVT is congruent to triangle UVT, then proving B), C), and D) can be done using the properties of congruent triangles. <BR>\n" );
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document.write( "There are several ways you can prove part A). Here's one:<BR>\n" );
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document.write( "You have already said ST and TU are congruent. <BR>\n" );
document.write( "Furthermore, you have correctly said SV is congruent to VU by definition of midpoint. <BR>\n" );
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document.write( "Now note that TV is a common side in the triangles STV and UTV. And TV is congruent to TV: Identity<BR>\n" );
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document.write( "All you need to do now is say that triangle STV is congruent to triangle UTV using side-side-side congruent to side-side-side.<BR>\n" );
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document.write( "Note that you can now say that D) is true, Angle S is congruent to Angle U because corresponding parts of congruent triangles are congruent.<BR>\n" );
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document.write( "Or another way you could have proven A) is to also to begin with the statements you have already made:<BR>\n" );
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document.write( "ST congruent to UT: Given<BR>\n" );
document.write( "V is the midpoint of SU: Given<BR>\n" );
document.write( "SV is congruent to VU: Def. Of midpoint<BR>\n" );
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document.write( "Then add the following (presuming you already have studied these properties):<BR>\n" );
document.write( "Triangle STV is isoseles: Given<BR>\n" );
document.write( "You have already said ST congruent to UT: Given. So you can add that<BR>\n" );
document.write( "Angle S congruent to Angle U: Angles opposite of congruent sides in isosceles triangles are congruent. [However, this is item D) you are to prove and you are just stating a reason for item D). So probably the best way to do this problem is to use the side-side-side method and then use the results of that to prove D).]<BR>\n" );
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document.write( "And now you can say triangle STV is congruent to triangle UTV using side-angle- side congruent to side-angle-side using ST-Angle S-SV congruent to UT-Angle U-UV<BR>\n" );
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document.write( "Now that you have demonstrated A) you can go on to B) TV is perpendicular to SU by noting the following using appropriate words that your instructor will accept:<BR>\n" );
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document.write( "SU is a straight line (180 degrees)<BR>\n" );
document.write( "Angle SVU congruent to Angle UVT:Corresponding parts of congruent triangles<BR>\n" );
document.write( "mAngle SVU + mAngle UVT = 180 degrees<BR>\n" );
document.write( "Substitute mAngle SVU for its congruent counterpart mAngle UVT to get:<BR>\n" );
document.write( "mAngle SVU + mAngle SVU = 180<BR>\n" );
document.write( "2 * mAngle SVU = 180<BR>\n" );
document.write( "mAngle SVU = 180/2 = 90<BR>\n" );
document.write( "If mAngle SVU = 90 then its congruent mAngle UVT also equals 90 <BR>\n" );
document.write( "Therefore TV perpendicular to SU: definition of perpendicular.<BR>\n" );
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document.write( "On to C)TV bisects Angle STU.<BR>\n" );
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document.write( "Angle STV is congruent to Angle UTV: Corresponding parts of congruent triangles<BR>\n" );
document.write( "Therefore, TV bisects Angle STU: definition of angle bisector.<BR>\n" );
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document.write( "And finally D)Angle S is congruent to Angle U.<BR>\n" );
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document.write( "If you used the side-side-side congruent to side-side-side procedure for showing that triangle STV is congruent to triangle UTV then you can immediately say that Angle S is congruent to Angle U because corresponding parts (both angles and sides) of congruent triangles are congruent.<BR>\n" );
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document.write( "Hope this gives you enough information so that you can wade your way through this problem. You were off to a very good start with what you had done already. <BR>\n" );
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