Suppose these statements about two triangles are true: ∠G=∠S,∠R=∠T,and ∠M=∠N. Which statement is correct? Select all that apply.
A.The sides are congruent.
B.The sides are proportional.
C.ΔGRM is similar to ΔNST
D.ΔMGR is similar to ΔNST
c and a probably
Not A. Having equal angles does not make them congruent.
Not C, because the vertices are not listed in the proper order.
So, you picked the two answers which are false!
To determine which statement or statements are correct, we need to analyze the given information about the angles of the two triangles.
∠G = ∠S implies that the corresponding angles at vertex G and vertex S are equal.
∠R = ∠T implies that the corresponding angles at vertex R and vertex T are equal.
∠M = ∠N implies that the corresponding angles at vertex M and vertex N are equal.
Now let's go through each statement one by one:
A. The sides are congruent: We cannot conclude that the sides of the triangles are congruent based on the given information about the angles. The angles alone do not determine the equality of the sides.
B. The sides are proportional: Similar to statement A, we cannot determine that the sides of the triangles are proportional based solely on the given angle information.
C. ΔGRM is similar to ΔNST: This statement is correct. If all three pairs of corresponding angles in two triangles are equal, then the triangles are similar. In this case, ∠G = ∠S, ∠R = ∠T, and ∠M = ∠N, so we can conclude that ΔGRM is similar to ΔNST.
D. ΔMGR is similar to ΔNST: This statement is not correct. The given information shows that ∠M = ∠N, but there is no information about the angle at vertex G, so we cannot determine if ΔMGR is similar to ΔNST.
Therefore, the correct statement is C. ΔGRM is similar to ΔNST.