Justify the last two steps of the proof. The image shows a quadrilateral R T U S with a horizontal diagonal drawn from S on the left to T on the right. Point R is the upper vertex and point U is the lower vertex. Given modifying above R S with bar is congruent to modifying above U T with bar and modifying above R T with bar is congruent to modifying above U S with bar Prove triangle R S T is congruent to triangle U T S Proof: first row: first column: modifying above R S with bar is congruent to modifying above U T with bar, second column Given second row first column: modifying above R T with bar is congruent to modifying above U S with bar, second column Given third row first column: modifying above S T with bar is congruent to modifying above T S with bar, second column question mark fourth row first column: triangle R S T is congruent to triangle U T S, second column question mark (4 points)
To analyze the last two steps, let's first label the given information:
Given: modifying above RS with bar is congruent to modifying above UT with bar (1)
Given: modifying above RT with bar is congruent to modifying above US with bar (2)
Now let's analyze the steps:
Third row, first column: modifying above ST with bar is congruent to modifying above TS with bar.
This step is not explicitly given, but it follows from the fact that ST and TS are just the reverse order of each other, so their modifications above the respective segments will be congruent.
Fourth row, first column: triangle RST is congruent to triangle UTS.
This step is justified by the fact that we have congruent pairs of corresponding sides: RS ≅ UT (from step 1) and RT ≅ US (from step 2), and we also have the congruent pair of corresponding angles T (common angle). Therefore, by the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle RST is congruent to triangle UTS.
In summary, the last two steps are justified based on the given information and the congruence postulate or criterion.