Question 1:
Hello,
to question 2:
I've modified your drawing (see attachment):
The angle in red is an exterior angle of the isosceles triangle ACD;
the angle in blue is an exterior angle of the isosceles triangle ABD.
The angle at the centre is 2x + 2y = 2(x+y) that means it is twice as large as the angle at C.
2. Observe the relationship between the elements of Diagonal 1 and Diagonal 2 in Pascal’s Triangle, shown on the next page. The sum of the first two elements in Diagonal 1 is equal to the second element in Diagonal 2. Similarly, the sum of the first 5 elements of Diagonal 1 is equal to the 5th element of Diagonal 2. Suppose we wish to use Pascal’s Triangle to find the sum of the first n natural numbers. Use combinatorial notation to express the sum of the n elements of Diagonal 1 in terms of the corresponding value in Diagonal 2.
3. Using the method of mathematical induction, prove that the following statements are false.