**Frank ICSE Solutions for Class 9 Maths Mid-point and Intercept Theorems Ex 15.2**

**Ex No: 15.2**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

Note: This question is incomplete.

According to the information given in the question,

F could be any point on BC as shown below:

So, this makes it impossible to prove that DP = DE, since P too would shift as F shift because P too would be any point on DE as F is.

Note: If we are given F to be the mid-point of BC, the result can be proved.

**Solution 7:**

From the figure EF ∥ AB and E is the midpoint of BC.

Therefore, F is the midpoint of AC.

Here EF ∥ BD, EF = BD as D is the midpoint of AB.

BE ∥ DF, BE = DF as E is the midpoint of BC.

Therefore BEFD is a parallelogram.

Remark: Figure modified

**Solution 8:**

**Solution 9:**