8. How many distinct triangles can you draw which have one side of length 3 cm , one side of length 6 cm , and one side of length 7 cm ? (A) None (B) One (C) Three (D) Infinitely many

To determine how many distinct triangles can be drawn with sides of lengths **3 cm**, **6 cm**, and **7 cm**, we need to examine the **Triangle Inequality Theorem**. This theorem states that for any three lengths to form a valid triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Let's verify this for the given lengths: 1. **3 cm + 6 cm > 7 cm** \[ 3 + 6 = 9 > 7 \] This holds true. 2. **3 cm + 7 cm > 6 cm** \[ 3 + 7 = 10 > 6 \] This also holds true. 3. **6 cm + 7 cm > 3 cm** \[ 6 + 7 = 13 > 3 \] This is true as well. Since all three conditions of the Triangle Inequality Theorem are satisfied, a triangle with these side lengths **can** exist. Furthermore, when the lengths of all three sides of a triangle are specified (a scenario known as **SSS - Side-Side-Side**), the triangle is uniquely determined **up to congruence**. This means there's only one distinct triangle (in terms of shape and size) that can be formed with these exact side lengths. **Answer:** **(B) One**