In the traingle CDE above, AD=BE and CD<CE. Which of the following is true?
Without knowing the options, we can conclude the following:
1. AD=BE: This means that the side AD is congruent to the side BE. It implies that triangle ADE is congruent to triangle BDE by the Side-Side-Side (SSS) congruence postulate.
2. CD<CE: This means that the length of side CD is less than the length of side CE.
Therefore, in triangle CDE:
- The sides AD and BE are congruent (AD = BE).
- The length of side CD is less than the length of side CE (CD < CE).
Based on the information provided, we know that AD=BE, which means that the lengths of sides AD and BE are equal.
We also know that CD < CE, which means that the length of side CD is smaller than the length of side CE.
Since we have a triangle CDE, the lengths of the sides form a triangle inequality. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, CD is smaller than CE, so we can say that CD + DE > CE. This is a true statement.
Therefore, the correct answer is that CD + DE > CE.