Question

Are the triangles PQR and RST similar why or why not?

Answer 1

Triangle PQR and RST are both right triangles but they do not share the same side lengths. They also share the same point R, so I would say that they are similar only because they are both right triangles.

Step-by-step explanation:

Answer 2

Answer: The triangles are similar

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Step-by-step explanation:

The square markers show that

angle RPQ = angle RST = 90 degrees

So that's one pair of congruent angles. Another pair of congruent angles is what you see in the diagram below. The angles marked in red are congruent alternate interior angles. Alternate interior angles are congruent when we have parallel lines like this.

Since we have two pairs of congruent angles, we can use the AA (angle angle) similarity theorem to prove the triangles congruent.