Question

which of these statements is true?
a to know whether 2 triangles are similar, it is enough to know the measure of 1 angle.
b to know whether 2 triangles are similar, it is enough to know the length of 1 side.
c to know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each tri
d to know whether 2 triangles are similar, it is enough to know the measure of 2 sides in each trian

Explanation:

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

• Option A: Knowing only one angle is not sufficient. For example, if we have two triangles, one with angles \(30^{\circ}, 60^{\circ}, 90^{\circ}\) and another with \(30^{\circ}, 40^{\circ}, 110^{\circ}\), just knowing the \(30^{\circ}\) angle is not enough to establish similarity.
• Option B: Knowing the length of one side is not sufficient for similarity. Similarity is about the ratio of sides and equality of angles. Just a single side length gives no information about angles or the ratio of other sides.
• Option C: If two angles of one triangle are equal to two angles of another triangle, then the third angle (since the sum of angles in a triangle is \(180^{\circ}\)) of the first triangle is equal to the third angle of the second triangle. By the AA similarity criterion, the two triangles are similar.
• Option D: Knowing the measure of two sides is not sufficient. We need to know the ratio of the sides and also information about angles (either through the SAS similarity criterion which requires the included angle or other angle - related information).

Answer:

C. To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.