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Mathematics

1 answer:

uranmaximum [27]3 years ago

3 0

Answer:

I hope this makes sense, sorry for the lack of proofs.

Step-by-step explanation:

It is given that S is the midpoint of line QT. The definition of a midpoint is that it bisects the line it is on. So, line QS and line TS are congruent, or the same.

Now, we also know that line QR and line TU are parallel. Because they are parallel, it means that they form congruent corners with lines QS and TS..I think the proof here is "angles opposite to congruent sides are congruent in a triangle." But I'm not sure if this is right. Anyways, this means angles RQS and UTS are congruent.

There's also some proof that when two lines cross, the opposite angles are congruent. This means that angles TSU and QSR are congruent.

Therefore, by ASA (angle-side-angle) ΔQRS ≅ ΔTUS.

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Step-by-step explanation:

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