Consider the statements one at a time. Redraw the diagram isolating the triangles when necessary.
C
Practice makes perfect
Let's investigate the statements one at a time.
Statement A
Consider the given diagram.
Regarding line segments, we only know that TS ≅ VU. Conversely, statement A says that TU and UV are congruent segments. We do not have enough information to assure this. Therefore, this statement is not true.
Statement B
Let's only consider â–³ STV and â–³ XVW.
We have no information about the angles or sides of â–³ XVW. Therefore, we cannot state that â–³ STV and â–³ XVM are congruent. This statement is false.
Statement C
Let's redraw the diagram separating the overlapping triangles.
By the Right Angles Congruence Theorem, we have that ∠STU ≅ ∠UVW. Moreover, we see that TS ≅ VU, and that ∠TSV ≅ VUW. This means the triangles have two pairs of congruent angles and one pair of congruent included sides. Therefore, △ TVS ≅ △ VWU by the ASA Congruence Theorem. This statement is true.
Statement D
As we already explained, the mentioned triangles are congruent. However, in this statement, the vertices have been named in the incorrect order. Therefore, corresponding parts do not appear in the same order. If it was true that △ VST ≅ △ VUW, then ST would be congruent to UW.
As we can see above, we do not have information to say that ST is congruent to UW. In fact ST is a leg of a right triangle and UW is the hypotenuse of a congruent right triangle. Therefore, they are actually not congruent. Statement D is not true.
