13. Analyze the two triangles in diagram 13.

Analysis of Figure 13:

• The figure presents two triangles: triangle ABC and triangle KMN.
• Triangle ABC has sides AC = 3.2, AB = 3, and Angle A = 70°. The side lengths are given with decimal precision, and one angle is provided.
• Triangle KMN has sides MN = 6, KN = 6.4, and Angle N = 70°.
• Comparing the two triangles, we observe that they share a common angle, Angle A = Angle N = 70°.
• Let's check for similarity using the SAS (Side-Angle-Side) criterion. We need to see if the ratio of the sides adjacent to the equal angles is the same.
• Ratio of sides in triangle ABC: AC/AB = 3.2 / 3 ≈ 1.067.
• Ratio of sides in triangle KMN: KN/MN = 6.4 / 6 ≈ 1.067.
• Since the ratios of the corresponding sides adjacent to the equal angle are equal (AC/AB = KN/MN), and the included angles are equal (Angle A = Angle N), the two triangles ABC and KMN are similar by the SAS similarity criterion.