Question

\( D \) and \( E \) are the midpoints of sides \( AB \) and \( AC \) of a triangle \( ABC \) respectively and \( BC = 10 \) cm. If \( DE \parallel BC \), then the length of \( DE \) is

• A. \( 3 \) cm
• B. \( 5 \) cm
• C. \( 4 \) cm
• D. \( 6 \) cm

Hint:

The Midpoint Theorem is a fundamental concept in geometry related to triangles. Remember that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

Answer 1

The Correct Option is B

Step 1: Recall the Midpoint Theorem.
The Midpoint Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side. Step 2: Apply the Midpoint Theorem to the given triangle.
In triangle \( ABC \), \( D \) is the midpoint of side \( AB \), and \( E \) is the midpoint of side \( AC \). According to the Midpoint Theorem, the line segment \( DE \) is parallel to the third side \( BC \), and its length is half the length of \( BC \). Step 3: Calculate the length of \( DE \).
Given that \( BC = 10 \) cm, the length of \( DE \) is: \[ DE = \frac{1}{2} BC \] \[ DE = \frac{1}{2} (10 \text{ cm}) \] \[ DE = 5 \text{ cm} \] The length of \( DE \) is 5 cm.