Answer for the first drop-down box is: SAS
Answer for the second drop-down box is: CPCTC
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Further Explanation:
We have these three facts:
Fact 1: RS = TU (given; shown by the red tick single tickmarks)
Fact 2: Angle TUW = Angle SRW (given; shown by the red arc markings)
Fact 3: SU = TR (proven in the paragraph proof provided)
Using those three facts together, we can use the SAS (side angle side) congruence theorem. Facts 1 and 3 provide the "S" portions of SAS; while fact 2 handles the "A" part. This is important: notice how the angle is between the two sides mentioned. The red angle R is between SR and RT. Similarly, the red angle U is between SU and TU
So this is why the first drop-down box is SAS
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The second drop-down box is CPCTC which stands for Corresponding Parts of Congruent Triangles are Congruent
In a nutshell, if two triangles are congruent, then the corresponding pieces must be as well. Think of two identical houses. If they are perfect clones of one another, then the front doors must be identical. In this analogy, the "house" is the whole "triangle"; the "door" is some part such as an angle or side of the triangle.
In this case, we take the fact that triangle TRS is congruent to triangle SUT which leads us to conclude that the corresponding angles RST and UST must also be equal by CPCTC.
