In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step.
6. A line parallel to side BC of a triangle ABC ,intersects AB and AC at D and E respectively. Prove that `(AD)/(DB)=(AE)/(EC)`.

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 1 . Prove that the sum of two consecutive odd numbers is divisible by 4.

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 4. Let x and y be rational numbers. Show that xy is a rational number.

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 5. If a and b positive integers, then you know that a =bq +r, 0 £ r lt b , where q is a whole number. Prove that HCF (a,b) =HCF (b,r).

XY is a line parallel to side BC of a triangle ABC. If BF ||AC and CF || AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF)

The incircle of an isosceles triangle ABC in which AB=AC , touches the sides BC, CA, and AB at D, E, and F respectively. Prove that BD=DC .

D and E are points on sides AB and AC respectively of tirangle ABC such that ar (DBC) = ar (EBC) . Prove that DE || BC

D and E are points on the sides CA and CB respectively of a triangle ABC right angale at C. prove that AE^(2)+BD^(2)=AB^(2)+DE^(2).

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=-1

For each of the following statements, determine whether an inclusive ''Or'' or exclusive ''Or'' is used. Give reasons for your answer. Two lines intersect at a point or are parallel.

D and E are points on sides AB and AC respectively of Delta ABC such that ar (DBC) = ar EBC). Prove that DE |\| BC.