https://file.aiquickdraw.com/mathbot/file/17297810645186t9xk1pj.jpg

The problem asks to construct a triangle \( \triangle ABC \) with the following conditions:
1. \( BC = 5 \, \text{cm} \)
2. \( \angle ABC = 100^\circ \)
3. \( AC - AB = 2.5 \, \text{cm} \)

### Steps for construction:
1. **Draw the base \( BC = 5 \, \text{cm} \):**
   - Use a ruler to draw a straight line segment \( BC \) of 5 cm.

2. **Construct \( \angle ABC = 100^\circ \):**
   - Place the protractor at point \( B \).
   - Measure and mark a point at \( 100^\circ \) from line \( BC \).
   - Draw a ray from \( B \) passing through this marked point. This ray will represent the direction of \( AB \).

3. **Determine points \( A \) along this ray:**
   - Use a compass to measure the difference \( AC - AB = 2.5 \, \text{cm} \).
   - Along the ray \( AB \), find the position where the difference in length between \( AC \) and \( AB \) is 2.5 cm. You can do this by trial and error using the compass, measuring and testing different positions along the ray to satisfy the condition.

4. **Complete the triangle:**
   - After finding point \( A \) on the ray \( AB \), connect point \( A \) to points \( B \) and \( C \) to form the triangle \( \triangle ABC \).

Would you like more detailed steps, or do you have any further questions on the construction process?

---

Here are 5 related questions to deepen your understanding:
1. How would the construction change if \( \angle ABC \) were an acute angle instead of obtuse?
2. What geometric principles ensure that the construction is accurate for the given conditions?
3. How would you verify the solution using measurements?
4. Can you solve for the lengths of \( AB \) and \( AC \) using the given condition \( AC - AB = 2.5 \, \text{cm} \)?
5. What happens if the difference between \( AC \) and \( AB \) is negative?

**Tip:** When dealing with angles in triangle constructions, always double-check the protractor's alignment to avoid errors in measurement.

Construct a triangle ABC in which BC = 5 cm, ∠ABC = 100° and AC - AB = 2.5 cm.

Learn how to construct triangle ABC where BC = 5 cm, the angle ABC = 100°, and the difference between AC and AB is 2.5 cm. This geometric construction involves angle measurement and side comparison, ideal 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