Question

4 practice 4 (from unit 3, lesson 10)
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 triangle.
d to know whether 2 triangles are similar, it is enough to know the measure of 2 sides in each triangle.
how did i do?

Explanation:

Step1: Recall triangle similarity criteria

Triangle similarity can be determined by AA (Angle - Angle) criterion. If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Step2: Analyze each option

• Option A: Knowing only 1 angle is not sufficient. There are infinitely many non - similar triangles with one equal angle.
• Option B: Knowing the length of 1 side is not sufficient. Similarity is about the ratio of sides and equality of angles.
• Option C: By AA criterion, if two angles of one triangle are equal to two angles of another triangle, the third angles (since the sum of angles in a triangle is \(180^{\circ}\)) will also be equal. So, knowing the measure of 2 angles in each triangle is enough.
• Option D: Knowing the measure of 2 sides in each triangle is not sufficient. We also need to know the included angle (for SAS similarity) or more information about the ratio of sides and angles.

Answer:

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