Triangles Unit Test 11 of 1211 of 12 Items Question In triangle ABD , AB is 3 cm long and BD is 5 cm long. According to the Triangle Inequality Theorem, which two lengths are possible lengths of AD ? (1 point) Responses 1 cm 1 cm 2 cm 2 cm 4 cm 4 cm 7 cm 7 cm 10 cm 10 cm

Answer 1

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

In triangle ABD, AB = 3 cm, BD = 5 cm.

So, for AD:
- The sum of AB and AD must be greater than BD: 3 + AD > 5
- The sum of BD and AD must be greater than AB: 5 + AD > 3

By solving these inequalities, we get:
3 + AD > 5
AD > 2

5 + AD > 3
AD > -2

Therefore, AD can have the possible lengths of 2 cm or any length greater than 2 cm. So, the correct answer is 2 cm and greater.