Step-by-step explanation:
I don't see all the options.
I only see the options under "angles", as it seems.
anyway, the way to prove this is :
the official definition of similar triangles is :
two triangles are said to be similar if their corresponding angles are congruent (and the corresponding sides are in proportion - but that is automatically true, when all 3 angles are matching).
so, if two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. we know this, because if two angle pairs are the same, then the third pair must also be equal (remember, the sum of all angles in a triangle is always 180°). When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
now, we look at the 2 triangles.
the angles QPR and STR are congruent (the same size).
we know also the angles QRP and SRT : they are both 90° and therefore congruent.
and that means that also the third angles PQR and RST are equal and therefore congruent (due to the 180° sum rule).
so, we have all 3 pairs of angles to be congruent, and the two triangles are therefore similar.
