Construct any right-angle triangle ABC. Let angle A be the right angle. Construct a line AD
perpendicular to side BC and draw it

To construct a right-angled triangle \( \triangle ABC \) with \( \angle A \) as the right angle and then construct a line \( AD \) perpendicular to side \( BC \), follow these steps:

### Steps for Construction:

1. **Draw the Triangle \( \triangle ABC \):**
   - Start by drawing a horizontal line segment \( AB \) as one leg of the triangle.
   - From point \( A \), draw a vertical line segment \( AC \) such that \( \angle A = 90^\circ \). \( AC \) is the other leg of the triangle.
   - Connect points \( B \) and \( C \) to complete the triangle.

2. **Construct Line \( AD \) Perpendicular to \( BC \):**
   - Identify point \( D \) on side \( BC \) such that \( AD \) is perpendicular to \( BC \).
   - From point \( A \), draw a line segment \( AD \) such that \( \angle DAB = 90^\circ \) and \( \angle DAC = 90^\circ \). This ensures \( AD \) is perpendicular to \( BC \).

### Explanation:
- The triangle \( \triangle ABC \) has \( \angle A = 90^\circ \), making it a right-angled triangle.
- \( AD \) is drawn perpendicular to \( BC \), meaning \( \angle DAB \) and \( \angle DAC \) are both right angles, ensuring that \( AD \) is the altitude from \( A \) to \( BC \).

Would you like a detailed diagram of this construction?

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### Related Questions:
1. How do you find the length of \( AD \) if the lengths of \( AB \) and \( AC \) are known?
2. What are the properties of the right-angled triangle \( \triangle ABC \) with respect to the altitude \( AD \)?
3. How can the area of \( \triangle ABC \) be calculated using \( AD \)?
4. What is the relationship between the angles in \( \triangle ABC \) and the segments formed by \( AD \) on \( BC \)?
5. How does the Pythagorean theorem apply to \( \triangle ABC \)?

### Tip:
Remember that in a right triangle, the altitude from the right angle to the hypotenuse divides the triangle into two smaller similar triangles, each of which is similar to the original triangle.

Learn how to construct a right-angled triangle ABC with angle A as the right angle and draw a perpendicular line AD to side BC. This construction involves key geometric concepts such as right-angled triangles and perpendicular lines. Suitable for students in Grades 7-9.

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