Question

If ΔJKL is congruent to ΔMNO and Δ ΜNΟ is congruent to Δ PQR which of the following must be true?

a)Δ LKJ is congruent to Δ RQP
b) ΔLKJ is congruent toΔPQR
C)Δ LKJ is congruent to Δ OMN
D)Δ ABC is congruent to Δ DEF​

Answer 1

Option (a) Δ LKJ is congruent to Δ RQP must be true because of the transitive property of congruence in geometry. Options (b) and (c) are incorrect because they do not correspond to the original congruence statement and the ordering of vertices, and option (d) is about unrelated triangles.

Step-by-step explanation:

If ΔJKL is congruent to ΔMNO and ΔMNO is congruent to ΔPQR, then it must be true that ΔLKJ is congruent to ΔRQP. This follows from the transitive property of congruence in geometry, which states that if one geometric figure is congruent to a second and the second is congruent to a third, then the first and third figures are also congruent. Therefore, option (a) Δ LKJ is congruent to Δ RQP must be true. Congruence preserves the order of the vertices, so it should be noted that Δ LKJ is the same as Δ JKL, just with the vertices listed in a different order.

Option (b) implies a congruence without reordering which is not the case here, and option (c) lists the triangles with vertices in an order that does not match with the original congruence statement. Option (d) refers to unrelated triangles and does not necessarily follow from the given information.