Question 1177132
**1. Given Information**

* Triangle ABC is scalene. This means that all three sides of the triangle have different lengths.
* AE and CD are altitudes of triangle ABC. This means that AE is perpendicular to BC, and CD is perpendicular to AB.

**2. Assumption**

Let's assume, for the sake of contradiction, that AE is congruent to CD.

**3. Area of a Triangle**

The area of a triangle can be calculated as (1/2) * base * height.

**4. Applying the Area Formula**

* Area of triangle ABC using base BC and altitude AE: (1/2) * BC * AE
* Area of triangle ABC using base AB and altitude CD: (1/2) * AB * CD

**5. Using the Assumption**

Since we assumed AE ≅ CD, we can substitute AE for CD in the area formulas:

* (1/2) * BC * AE = (1/2) * AB * AE

**6. Simplifying the Equation**

If we divide both sides of the equation by (1/2) * AE, we get:

* BC = AB

**7. Contradiction**

This result contradicts our given information that triangle ABC is scalene (meaning all sides have different lengths).

**8. Conclusion**

Therefore, our initial assumption that AE ≅ CD must be false. Hence, we have proven that AE is not congruent to CD.