Question

1. which of these statements is true? (lesson 3 - 10)

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 triangle.
d. to know whether 2 triangles are similar, it is enough to know the measure of 2 sides in each triangle.

Explanation:

• For option A: Knowing only one - angle measure is not sufficient for triangle similarity. There are infinitely many non - similar triangles with one angle of the same measure.
• For option B: Knowing the length of one side is not enough. Similarity is based on angle - angle - angle (AAA) or side - angle - side (SAS) similarity ratios etc., not just a single side length.
• For 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 two triangles will also be equal. By the AA (angle - angle) similarity criterion, the two triangles are similar.
• For option D: Knowing the measure of two sides without the included angle (or other proper angle - side relationships) is not enough for similarity. For example, we could have two triangles with two sides of the same length but different included angles, resulting in non - similar triangles.

Answer:

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