# SOLUTION: I'm having a little trouble with trying to figure this problem out Given: Isos. Triangle STU ST is congruent to TU V is the midpoint of SU Prove: a)triangle svt is congruent t

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: I'm having a little trouble with trying to figure this problem out Given: Isos. Triangle STU ST is congruent to TU V is the midpoint of SU Prove: a)triangle svt is congruent t      Log On

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 Click here to see ALL problems on Geometry proofs Question 548932: I'm having a little trouble with trying to figure this problem out Given: Isos. Triangle STU ST is congruent to TU V is the midpoint of SU Prove: a)triangle svt is congruent to triangle uvt B)tv is perpendicular to su C)tv bisects angle stu D) angle s is congruent to angle u All I can get is: ST is congruent to TU:Given V is the midpoint of SU:Given SV is congruent to VU:Def. Of midpoint I'm stuck on what to do next. Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!You said: . ST is congruent to TU: Given <--- Good V is the midpoint of SU: Given <--- Good SV is congruent to VU: Def. Of midpoint <--- Good I'm stuck on what to do next. . 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. . There are several ways you can prove part A). Here's one: . You have already said ST and TU are congruent. Furthermore, you have correctly said SV is congruent to VU by definition of midpoint. . Now note that TV is a common side in the triangles STV and UTV. And TV is congruent to TV: Identity . 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. . 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. . Or another way you could have proven A) is to also to begin with the statements you have already made: . ST congruent to UT: Given V is the midpoint of SU: Given SV is congruent to VU: Def. Of midpoint . Then add the following (presuming you already have studied these properties): Triangle STV is isoseles: Given You have already said ST congruent to UT: Given. So you can add that 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).] . 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 . 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: . SU is a straight line (180 degrees) Angle SVU congruent to Angle UVT:Corresponding parts of congruent triangles mAngle SVU + mAngle UVT = 180 degrees Substitute mAngle SVU for its congruent counterpart mAngle UVT to get: mAngle SVU + mAngle SVU = 180 2 * mAngle SVU = 180 mAngle SVU = 180/2 = 90 If mAngle SVU = 90 then its congruent mAngle UVT also equals 90 Therefore TV perpendicular to SU: definition of perpendicular. . On to C)TV bisects Angle STU. . Angle STV is congruent to Angle UTV: Corresponding parts of congruent triangles Therefore, TV bisects Angle STU: definition of angle bisector. . And finally D)Angle S is congruent to Angle U. . 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. . 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. .