Question

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

Answer 1

D.ΔMGR is similar to ΔNST

Explanation:

Since, ∠G = ∠S, ∠R = ∠T, and ∠M = ∠N

Thus we use Angle-Angle-Angle (AAA) property of triangle,

The Angle-Angle-Angle (AAA) property of triangle states that when all angles of one triangle is equal to all angles of other triangle then both triangle is similar to each other. This property is also called Angle-Angle(AA) Property.

Thus, ΔMGR is similar to ΔNST

Option (D) is correct.

Also, option (C) is not correct because name of triangle is written in wrong order. By this name it conclude that, ∠G = ∠N, ∠R = ∠S, and ∠M = ∠T. which is not true.

Answer 2

B. The sides are proportional.

D. ΔMGR is similar to ΔNST.

Explanation:

If two triangles have corresponding angles equal, the triangles are similar.

If two triangles are similar, their corresponding sides are proportional.

A is wrong. The sides could be congruent in the special case of identical triangles, but similar triangles are not usually identical,

C is wrong. When you name similar triangles, the order of the letters of corresponding angles must be in matching order. ∠G ≠ ∠N.