Given that qp congruent to sr and qr congruent to st, which theorem or postulate proves δpqr congruent to δrst?

a) asa congruence postulate
b) sas congruence postulate
c) hl congruence theorem
d) sss congruence postulate

Hey there!

The answer is B) SAS Congruence Postulate.

SAS Congruence Postulate: If two sides and their inclusive angle is congruent to the corresponding two sides and inclusive angle of another triangle, then they are congruent.

Segment QP is congruent and corresponding to segment SR, while segment QR is congruent and corresponding to ST.

The inclusive angles are the angles marked to be right angles. They are inclusive because the angle is formed by those two sides that are being referred to.

The angles are congruent because they are both right angles. We can see that by looking at the little square-ish markings in the angle.

This means that ΔPQR can be proved congruent to ΔRST through SAS congruence postulate.

Hope this helps!

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.