Question on Solving a Problem using Proportion Method

Topic : Proportion Method

Question : Fuji apples cost $2.10 for 3 lb. Us a proportion to find how much it would cost to buy 7 lb. By proportion method :

Solution :
2.10/3 = ?/7
0.7 x 7=$ ?
$ 4.9 will be the cost of 7 Fuji Apples$

Topic : Parallelogram

Question : If ABCD is a parallelogram with equal diagonals, then prove that ABCD is a rectangle.

Solution :

Given ABCD is a parallelogram AC = BD

To prove : ABCD is a rectangle

Proof : In ∆ABD and ∆BCA

AD = BC (opposite sides of a parallelogram are equal)

BD = AC (given)

AB = AB

Therefore by SSS theorem of congruency

∆ADB congruent to ∆BCA

So ∟DAB = ∟CBA (corresponding angles of congruent triangles)

Now ∟DAB + ∟CBA = 180º (sum of consecutive angles of a parallelogram is 180º)

So ∟DAB =∟CBA = 180º/2 = 90º

If one of the angle of a parallelogram is a right angle then the parallelogram is a rectangle.

Hence ABCD is a rectangle.