To determine whether line $AB$ is longer than line $BC$ in triangle $ABC$, we need to consider the properties of the triangle and the given angles.

Key Information Recap

• Triangle $ABC$ is a right triangle with a right angle at $C$ ($\angle ABC = 90^\circ$).
• $\angle ADB = 70^\circ$, which implies that $\angle ACB = 20^\circ$ and $\angle BAC = 70^\circ$.

Analyzing Triangle $ABC$

1. Right Triangle Properties:

   • In a right triangle, the side opposite the largest angle (which is 90 degrees) is the hypotenuse. This hypotenuse is always the longest side.
   • Here, $AB$ is the hypotenuse since it is opposite the right angle $\angle ABC = 90^\circ$.

2. Comparing Sides $AB$ and $BC$:

   • $AB$ is the hypotenuse, so it must be longer than either leg of the triangle.
   • $BC$ is one of the legs of the triangle, and the other leg is $AC$.

Since $AB$ is the hypotenuse of the right triangle $ABC$, line $AB$ is longer than line $BC$.

Would you like more details or have any questions about this solution?

Here are 5 related questions that expand on this information:

1. How do you find the length of the hypotenuse in a right triangle using the Pythagorean theorem?
2. How do you calculate the length of a side in a right triangle if you know the hypotenuse and one other side?
3. What are the properties of the legs of a right triangle compared to the hypotenuse?
4. Can a right triangle have two sides of equal length?
5. How do the trigonometric ratios (sine, cosine, and tangent) relate to the sides of a right triangle?

Tip: In a right triangle, the hypotenuse is always longer than either of the other two sides.