Question

1. finish this sentence stater by choosing which of these statements is true? to know whether 2 triangles are similar, it is enough to know...

a. the measure of 1 angle in each triangle. b. the length of 1 side in each triangle.
c. the measure of 2 angles in each triangle. d. the measure of 2 sides in each triangle.

Explanation:

Step1: Recall triangle similarity criteria

Triangle similarity (AA, SAS, SSS) – AA (Angle - Angle) similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Step2: Analyze each option

• Option A: One angle is not enough (e.g., two triangles with one \(30^\circ\) angle can have different other angles, not similar).
• Option B: One side length gives no info about angles or proportionality of sides, not enough for similarity.
• Option C: By AA similarity, if two angles of one triangle equal two angles of another, the third angles (since sum of angles in a triangle is \(180^\circ\)) must also be equal. So two angles being equal implies similarity.
• Option D: Two side lengths with no info about included angle or proportionality, not enough (e.g., sides \(2,3\) in one triangle and \(4,5\) in another – not similar).

Answer:

C. the measure of 2 angles in each triangle.