Answer:
The proof is explained step-wise below :
Step-by-step explanation :
For better understanding of the solution see the attached figure :
Given : ABCD is a Parallelogram ⇒ AB ║ DC and AD ║ BC
Now, F lies on the extension of DC. So, AB ║ DF
To Prove : ΔABE is similar to ΔFCE
Proof :
Now, in ΔABE and ΔFCE
∠ABE = ∠FCE ( alternate angles are equal )
∠AEB = ∠FEC ( Vertically opposite angles )
So, by using AA postulate of similarity of triangles
ΔABE is similar to ΔFCE
Hence Proved.
which means
has no solution, and we can omit that factor.
This leaves us with
which occurs for
.
It would be true no explanation needed
The product of two rational numbers is always rational because (ac/bd) is the ratio of two integers, making it a rational number.
We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.
Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".
P = (a/b)×(c/d)
P = (a×c)/(b×d)
The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.
learn more about of rational numbers here
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Answer:
yes they form a proportion
