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Explanation:
Focus on triangles SVT and UVT.
They are congruent triangles due to the fact that SV = VU and VT = VT. From there we can use the LL (leg leg) theorem for right triangles to prove them congruent.
Since the triangles are the same, just mirrored, this means ST = UT = 23.
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Following similar reasoning as the previous section, we can prove triangle RVU = triangle RVS.
Therefore, RS = RU = 8
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SV = VU = 5 because RT bisects SU.
Bisect means to cut in half. The two smaller pieces are equal.
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SU = SV + VU = 5+5 = 10
Refer to the segment addition postulate.
Answer:
ST=23
RU=8
SV=5
SU=10
Step-by-step explanation:
RT bisects the whole quadrilateral, so a line on one side will be the same length as the line on the opposite side of RT. So:
1. ST=UT, UT=23, so ST=23
2. RU=RS, RS=8, so RU=8
3. SV=VU, VU=5, so SV=5
4. SU=2*SV, 5*2=10, so SU=10
If you still have no clue, just imagine the points R, S, T, and the lines connecting them (this will make a triangle). Then reflect the triangle across line RT, and name the new S point U (the new triangle still has the same line measures) . Make a line from S to U and make a point V from where RT and SU meet. This will make the figure in the picture.
Have a nice day! :)