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.

Explore whether line AB is longer than line BC in triangle ABC using the properties of right triangles and the Pythagorean theorem. Understand how to apply these concepts to determine lengths in geometric shapes. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation