Question

(03.01 MC) PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent. Which fact is used to prove that angle PTR is always equal to angle STQ? (1 point) If two angles are equal to the same measure, then the angles are congruent. If two angles are equal to the same measure, then the angles are supplementary. Lines PQ and RS have a fixed length. Lines PQ and RS intersect at right angles.

Answer 1

Answer: If two angles are equal to the same measure, then the angles are congruent.

That is actually the definition of congruent. Whenever they throw the same value, they are called congruent.

There is something that proves that PTR and STQ will always be equal to the same measure, and it was not among the given options:

Acording to the construction protocol, one side of PTR (the PT side) is opposite to one side of STQ (the TQ side). We call two rays opposite when they belong to the same line but they have different directions (for example, one goes to the left and the other one goes to the right). Try building it and you will see it! The same happens with the other sides: TR is opposite to ST. Whenever this happens, we call those two angles a vertical pair and they are always the same size. You can prove that tying it up with linear pairs, which sum 180°. An angle forms a linear pair with another angle whenever they share a side and the other two sides are in the same line.

If a and b are supplementary angles, then a+b=180°

So a=180°-b

If b and c are adjacent angles, then b+c =180°

So c=180°-b

This proves that c and a are the same size.