Question

g.srt.b.5: similarity
577 triangle jgr is similar to triangle mst. which statement is not always true?

1. ∠j ≅ ∠m
2. ∠g ≅ ∠t
3. ∠r ≅ ∠t
4. ∠g ≅ ∠s

Explanation:

When two triangles are similar (△JGR ~ △MST), their corresponding angles are congruent. The order of the letters in the triangle names indicates the correspondence: ∠J corresponds to ∠M, ∠G corresponds to ∠S, and ∠R corresponds to ∠T.

• For option 1: ∠J ≅ ∠M (corresponding angles, true).
• For option 2: ∠G ≅ ∠T – ∠G corresponds to ∠S, not ∠T, so this is not always true.
• For option 3: ∠R ≅ ∠T (corresponding angles, true).
• For option 4: ∠G ≅ ∠S (corresponding angles, true).

Answer:

1. $\angle G \cong \angle T$